The function y=ax²+bx+c: Matching parameters

To solve this problem, we will identify the parameters of the given quadratic function step-by-step:

• Step 1: Define the problem statement: We have $y = x^2 + x + 5$.
• Step 2: Identify the standard form of a quadratic function, which is $y = ax^2 + bx + c$.
• Step 3: Compare the given quadratic expression with the standard form to identify the coefficients.

Now, let's analyze the quadratic function provided:

From the given expression $y = x^2 + x + 5$:
- The coefficient of $x^2$ is $1$, so $a = 1$.
- The coefficient of $x$ is $1$, so $b = 1$.
- The constant term is $5$, so $c = 5$.

Therefore, the parameters of the quadratic function are $a = 1$, $b = 1$, and $c = 5$.

Consequently, the correct choice from the provided options is $(a = 1, b = 1, c = 5)$.

To solve the problem of identifying the coefficients in the quadratic function $y = -x^2 + x + 5$, we follow these steps:

• Step 1: Write down the general form of a quadratic equation: $y = ax^2 + bx + c$.

• Step 2: Compare the given equation $y = -x^2 + x + 5$ to the general form.

• Step 3: Identify the value of each coefficient:

  • The coefficient of $x^2$ is $-1$, so $a = -1$.

  • The coefficient of $x$ is $+1$, so $b = 1$.

  • The constant term is $+5$, so $c = 5$.

Therefore, the parameters of the quadratic function are $a = -1$, $b = 1$, and $c = 5$.

This matches choice 2, confirming the parameters in the quadratic function.

Final Answer: $a=-1, b=1, c=5$.

To solve this problem, we'll follow these steps:

• Step 1: Compare the given quadratic function with the standard form.
• Step 2: Directly identify the coefficients $a$, $b$, and $c$.
• Step 3: Verify the correct choice from the provided options, if applicable.

Now, let's work through each step:
Step 1: The given quadratic function is $y = 3x^2 + 3x - 4$. The standard form for a quadratic equation is $y = ax^2 + bx + c$.
Step 2: By comparing the given equation to the standard form, we can identify the coefficients:
- $a = 3$, from the term $3x^2$.
- $b = 3$, from the term $3x$.
- $c = -4$, from the constant term $-4$.
Step 3: With these values, compare them to the given choices. The choice that matches these values is option 3: $a = 3, b = 3, c = -4$.

Therefore, the solution to the problem is $a = 3, b = 3, c = -4$.

To solve this problem, we'll compare the given quadratic function with its standard form:

• Step 1: Recognize the given function as $y = -4x^2 + 3$.
• Step 2: Write down the standard form of a quadratic function, which is $y = ax^2 + bx + c$.
• Step 3: Match corresponding terms to identify $a$, $b$, and $c$.

Now, let's work through these steps:

Step 1: The given function is $y = -4x^2 + 3$.

Step 2: The standard form of a quadratic function is $y = ax^2 + bx + c$.

Step 3: By direct comparison:
- The coefficient of $x^2$ in the given expression is $-4$. Therefore, $a = -4$.
- There is no $x$ term in the given expression, which implies the coefficient $b = 0$.
- The constant term in the given expression is $3$, indicating $c = 3$.

Therefore, the solution is $a = -4$, $b = 0$, $c = 3$, which matches with choice 3.

To solve this problem, we will follow these steps:

• Step 1: Identify the form of a standard quadratic equation.
• Step 2: Compare the given function with the quadratic standard form.
• Step 3: Match the coefficients to the given answer choices.

Now, let's work through each step:
Step 1: The standard form of a quadratic function is $y = ax^2 + bx + c$.
Step 2: Given the function $y = -3x^2 - 4$, we compare this with the standard form:

• Coefficient $a$ is associated with $x^2$. Here, $a = -3$.
• Coefficient $b$ is associated with $x$. Since there is no $x$ term, $b = 0$.
• The constant term $c$ is the standalone number, which is $c = -4$.

Therefore, the solution to the problem is $a = -3, b = 0, c = -4$.

To solve the problem, we'll identify the parameters $a$, $b$, and $c$ from the given quadratic function:

• **Step 1**: Compare the given equation $y = -5x^2$ with the general quadratic form $y = ax^2 + bx + c$.
• **Step 2**: Note that the coefficient of $x^2$ is $-5$, hence $a = -5$.
• **Step 3**: Since there is no $x$ term, $b = 0$.
• **Step 4**: Since there is no constant term, $c = 0$.

After identifying the parameters, we conclude:

The parameters for the quadratic function are $a = -5$, $b = 0$, $c = 0$. Therefore, the correct choice is:

The correct answer is $a = -5, b = 0, c = 0$.

To solve this problem, we will follow these steps:

• Step 1: Identify the given quadratic equation and its form.
• Step 2: Directly match the coefficients of the given equation to the standard form $y = ax^2 + bx + c$.
• Step 3: Compare with the provided choices and select the one that matches.

Now, let's work through each step:
Step 1: The given quadratic equation is $y = -x^2 + 3x + 40$. This matches the form $y = ax^2 + bx + c$.

Step 2: By comparing the given equation to the standard form:
- The coefficient $a$ is the coefficient of $x^2$, which is $-1$.
- The coefficient $b$ is the coefficient of $x$, which is $3$.
- The coefficient $c$ is the constant term, which is $40$.

Step 3: From the analysis, we identify $a = -1$, $b = 3$, $c = 40$. We compare these with the provided choices.
The correct answer is: $a=-1,b=3,c=40$

Therefore, the solution to the problem matches choice 4.

To solve this problem, we will identify values of $a$, $b$, and $c$ in the quadratic function:

• Step 1: Note the given equation $y = 3x^2 - 81$.
• Step 2: Compare it to the standard quadratic form $y = ax^2 + bx + c$.
• Step 3: Match coefficients to find $a$, $b$, and $c$.

Now, let's work through each step:
Step 1: The given equation is $y = 3x^2 - 81$.
Step 2: Compare this to the standard form, $y = ax^2 + bx + c$. In this equation:
- The coefficient of $x^2$ is 3, hence $a = 3$.
- There is no $x$ term, which means $b = 0$.
- The constant term is $-81$, hence $c = -81$.

Therefore, the solution to the problem is $a = 3, b = 0, c = -81$.

To solve this problem, let's follow these steps:

• Step 1: Recognize the standard form of a quadratic equation.
• Step 2: Match the given function to the standard form.
• Step 3: Identify each coefficient $a$, $b$, and $c$.

Now, let's work through these steps:

Step 1: The standard form of a quadratic function is $y = ax^2 + bx + c$. Our goal is to identify $a$, $b$, and $c$.

Step 2: We are given the function $y = x^2$. This can be aligned with the standard form as $y = 1 \cdot x^2 + 0 \cdot x + 0$.

Step 3: By comparing the given function $y = x^2$ with the standard form, we can deduce:
- The coefficient of $x^2$ is 1, so $a = 1$.
- The linear term coefficient is missing, which implies $b = 0$.
- There is no constant term, so $c = 0$.

Therefore, the coefficients are $a = 1, b = 0, c = 0$, corresponding to choice 1.

To solve this problem, we will follow these steps:

• Step 1: Identify each term in the given function $y = 2x^2 + 3$.
• Step 2: Compare the equation to the standard quadratic form $y = ax^2 + bx + c$.
• Step 3: Determine the coefficients $a$, $b$, and $c$.
• Step 4: Match these coefficients to the correct multiple-choice option.

Step 1: The given function is $y = 2x^2 + 3$. There is no $x$ term present.

Step 2: Compare this with the standard form $y = ax^2 + bx + c$:

• The coefficient of $x^2$ is $a = 2$.
• The coefficient of $x$ is $b = 0$ because there is no $x$ term.
• The constant term is $c = 3$.

Step 3: Therefore, the coefficients are $a = 2$, $b = 0$, and $c = 3$.

Step 4: Review the multiple-choice options provided:

• Choice 1: $a = 0$, $b = 2$, $c = 3$
• Choice 2: $a = 0$, $b = 3$, $c = 2$
• Choice 3: $a = 2$, $b = 0$, $c = 3$
• Choice 4: $a = 3$, $b = 0$, $c = 2$

The correct choice is Choice 3: $a = 2$, $b = 0$, $c = 3$.

Therefore, the solution to the problem is the values $a = 2$, $b = 0$, $c = 3$ which correspond to choice 3.

Here we have a quadratic equation.

A quadratic equation is always constructed like this:

$y = ax²+bx+c$

Where a, b, and c are generally already known to us, and the X and Y points need to be discovered.

Firstly, it seems that in this formula we do not have the C,

Therefore, we understand it is equal to 0.

$c = 0$

a is the coefficient of X², here it does not have a coefficient, therefore

$a = 1$

$b= 10$

is the number that comes before the X that is not squared.

To solve this problem, we'll clearly delineate the given expression and compare it to the standard quadratic form:

• Step 1: Recognize the standard form of a quadratic equation as $y = ax^2 + bx + c$.
• Step 2: Compare the given equation $y = x^2 - 6x + 4$ to the standard form.
• Step 3: Identify coefficients:
  - The coefficient of $x^2$ is $a = 1$.
  - The coefficient of $x$ is $b = -6$.
  - The constant term is $c = 4$.

Therefore, the coefficients for the quadratic function $y = x^2 - 6x + 4$ are $a = 1$, $b = -6$, and $c = 4$.

Among the provided choices, choice 3: $a=1,b=-6,c=4$ is the correct one.

In fact, a quadratic equation is composed as follows:

y = ax²-bx-c

That is,

a is the coefficient of x², in this case 2.
b is the coefficient of x, in this case 5.
And c is the number without a variable at the end, in this case 6.

To solve this problem, we'll follow these steps:

• Identify the given quadratic function.
• Match it with the standard form of a quadratic equation $y = ax^2 + bx + c$.
• Extract the values of $a$, $b$, and $c$ directly from the comparison.

Now, let's work through each step:
Step 1: The given quadratic function is $y = 2x^2 - 3x - 6$.
Step 2: The standard form of a quadratic equation is $y = ax^2 + bx + c$.
Step 3: By matching the given quadratic function with the standard form:

- The coefficient of $x^2$ is $2$, so $a = 2$.
- The coefficient of $x$ is $-3$, so $b = -3$.
- The constant term is $-6$, so $c = -6$.

Therefore, the solution to the problem is $a = 2$, $b = -3$, $c = -6$.

The given quadratic function is $y = 5x^2 - 4x - 30$.
To identify the coefficients, let's compare this with the standard form of a quadratic equation, $y = ax^2 + bx + c$.

• Step 1: Compare the terms of the given equation to the standard form.
• Step 2: Identify each coefficient:
  For $ax^2$, $a = 5$ in the term $5x^2$.
  For $bx$, $b = -4$ in the term $-4x$.
  For the constant term $c$, $c = -30$.

Thus, we have identified the coefficients as $a = 5$, $b = -4$, and $c = -30$.

Therefore, the correct answer is $a = 5, b = -4, c = -30$.

The correct choice is .

Let's determine the coefficients for the quadratic function given by $y = -2x^2 + 3x + 10$.

• Step 1: Identify $a$.
  The coefficient of $x^2$ is $-2$. Thus, $a = -2$.
• Step 2: Identify $b$.
  The coefficient of $x$ is $3$. Thus, $b = 3$.
• Step 3: Identify $c$.
  The constant term is $10$. Thus, $c = 10$.

Comparing these coefficients to the provided choices, the correct answer is:

$a = -2, b = 3, c = 10$ .

Therefore, the correct choice is Choice 4.

To solve this problem, we'll follow these steps:

• Step 1: Identify the given quadratic function.
• Step 2: Compare it to the standard form $y = ax^2 + bx + c$.
• Step 3: Determine the values of $a$, $b$, and $c$.

Now, let's work through each step:

Step 1: The problem gives us the quadratic function $y = 3x^2 + 4x + 5$.

Step 2: The standard form of a quadratic function is $y = ax^2 + bx + c$.

Step 3: By comparing $y = 3x^2 + 4x + 5$ with $y = ax^2 + bx + c$, we find:
- The coefficient of $x^2$ is $a = 3$.
- The coefficient of $x$ is $b = 4$.
- The constant term is $c = 5$.

Therefore, the solution to the problem is $a = 3, b = 4, c = 5$.

This matches choice 2, which states: $a = 3, b = 4, c = 5$.

To solve this problem, we need to express the given function $y = 5x + 3x^2$ in the standard quadratic form $y = ax^2 + bx + c$.

Let's match the components of $y = 5x + 3x^2$ with the standard form:

• The term $3x^2$ corresponds to $ax^2$, so $a = 3$.
• The term $5x$ corresponds to $bx$, so $b = 5$.
• There is no constant term in the equation, which means $c = 0$.

Therefore, the values of the coefficients are:

• $a = 3$
• $b = 5$
• $c = 0$

From the answer choices given, the correct choice is:

• Choice 3: $a = 3, b = 5, c = 0$

Therefore, the solution to the problem is $a = 3, b = 5, c = 0$.

Let's recall the general form of a quadratic function:

$y=ax^2+bx+c$

Examine the given function in the problem:

$y=6x-6x^2+3$$$

Note that in the general form of the quadratic function mentioned above, the terms are arranged from the highest power (which is the quadratic term - power of 2) to the lowest power (which is the free term - power of 0),

Therefore, in order to make it easier to identify the coefficients, we'll apply the commutative property of addition and rearrange the terms of the quadratic function so they are written from highest to lowest power:

$y=6x-6x^2+3 \\ y=-6x^2+6x+3$

We can then identify that the coefficient of the quadratic term, meaning the coefficient of the term with power two: $a$ is $-6$ We'll continue and identify that the coefficient of the term with power one: $b$ is $6$ and finally we'll identify that the coefficient of the term with power 0, meaning the free term: $c$ is $3$

To summarize, the coefficients in the given function are:

$a=-6,\hspace{4pt}b=6,\hspace{4pt}c=3$

Therefore, the correct answer is answer A.

Note:

The coefficient $c$is the free term - and we said before that it's the coefficient of the term with power zero - $x^0$this is because any number different from zero raised to the power of zero equals 1:

$x^0=1$, and therefore we could write the general form of the function above as:

$y=ax^2+bx+c \\ \downarrow\\ y=ax^2+bx+c\cdot1 \\ \downarrow\\ y=ax^2+bx^1+c x^0$

meaning, $c$ is the coefficient of the term with power 0.

To solve this problem, we'll start by rearranging the given equation:

• Step 1: Identify the standard quadratic form: $y = ax^2 + bx + c$.
• Step 2: Rearrange $6 = 6x + 2x^2$ to fit $ax^2 + bx + c = 0$.
• Step 3: Identify coefficients $a$, $b$, and $c$.

Now, let's work through each step:
Step 1: The general form we aim for is $y = ax^2 + bx + c$.
Step 2: Rearrange the given equation:
Start by rearranging the terms to resemble $ax^2 + bx + c = 0$. We write the equation as:
$2x^2 + 6x - 6 = 0$

Step 3: Now, comparing this with the standard form $ax^2 + bx + c = 0$, we identify the coefficients:
$a = 2$
$b = 6$
$c = -6$

Therefore, the correct parameters for the equation $6 = 6x + 2x^2$ are $a = 2$, $b = 6$, and $c = -6$.

Checking against the answer choices, choice 3: $(a=2, b=6, c=-6)$ matches our result.