Quadratic Function Practice Problems - Parabola Vertex & Graph

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 $a = -3, b = 0, c = -4$.