Quadratic Function Graphing Practice - Parameter a, b, c

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.

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.

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, 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'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.