What is the range of this quadratic function? y = x^2 - 8x + 12 Choices: (A){y | y ≤ -4} (B){y | y ≥ 4} (C){y | y ≥ -4} (D)all real numbers

Identify Quadratic Function: Identify the quadratic function. We have the quadratic function y = x^2 - 8x + 12.Find Vertex x-coordinate: Find the x-coordinate of the vertex. The x-coordinate of the vertex of a quadratic function in the form y = ax^2 + bx + c is given by x = -b/(2a). Here, a = 1 and b = -8. x = -(-8)/(2*1) x = 8/2 x = 4Find Vertex y-coordinate: Find the y-coordinate of the vertex. Substitute x = 4 into the quadratic function to find the y-coordinate. y = (4)^2 - 8*(4) + 12 y = 16 - 32 + 12 y = -16 + 12 y = -4Determine Parabola Direction: Determine the direction of the parabola. Since a = 1 and a > 0, the parabola opens upwards.Find Range of Function: Find the range of the function. The vertex of the parabola is (4, -4), and since the parabola opens upwards, the y-values must be greater than or equal to the y-coordinate of the vertex. Range: {y | y ≥ -4}

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What is the range of this quadratic function? $\newline$ $y = x^2 - 8x + 12$ $\newline$ Choices: $\newline$ (A) $\{y | y \leq -4\}$ $\newline$ (B) $\{y | y \geq 4\}$ $\newline$ (C) $\{y | y \geq -4\}$ $\newline$ (D)all real numbers

View step-by-step help

Home

Math Problems

Algebra 1

Domain and range of quadratic functions: equations

Full solution

Q. What is the range of this quadratic function?

\newline

y = x^2 - 8x + 12

\newline

Choices:

\newline

(A)

\{y | y \leq -4\}

\newline

(B)

\{y | y \geq 4\}

\newline

(C)

\{y | y \geq -4\}

\newline

(D)all real numbers

Identify Quadratic Function: Identify the quadratic function. $\newline$ We have the quadratic function $y = x^2 - 8x + 12$ .
Find Vertex x-coordinate: Find the x-coordinate of the vertex. $\newline$ The x-coordinate of the vertex of a quadratic function in the form $y = ax^2 + bx + c$ is given by $x = -\frac{b}{2a}$ . Here, $a = 1$ and $b = -8$ . $\newline$ $x = -(-8)/(2\cdot 1)$ $\newline$ $x = \frac{8}{2}$ $\newline$ $x = 4$
Find Vertex y-coordinate: Find the y-coordinate of the vertex. $\newline$ Substitute $x = 4$ into the quadratic function to find the y-coordinate. $\newline$ $y = (4)^2 - 8\times(4) + 12$ $\newline$ $y = 16 - 32 + 12$ $\newline$ $y = -16 + 12$ $\newline$ $y = -4$
Determine Parabola Direction: Determine the direction of the parabola. Since $a = 1$ and a > 0, the parabola opens upwards.
Find Range of Function: Find the range of the function. $\newline$ The vertex of the parabola is $(4, -4)$ , and since the parabola opens upwards, the $y$ -values must be greater than or equal to the $y$ -coordinate of the vertex. $\newline$ Range: \{ $y | y \geq -4$ \}