What is the range of this quadratic function? y = x^2 - 10x + 21 Choices: (A){y | y ≥ 5} (B){y | y ≤ 5} (C){y | y ≥ -4} (D)all real numbers

Identify Quadratic Function: Identify the quadratic function. We are given the quadratic function y = x^2 - 10x + 21.Find Vertex: Find the x-coordinate of the vertex. To find the vertex of the parabola, we use the formula x = -b/(2a), where a is the coefficient of x^2 and b is the coefficient of x. In this case, a = 1 and b = -10. x = -(-10)/(2*1) x = 10/2 x = 5Find Y-Coordinate: Find the y-coordinate of the vertex. Substitute x = 5 into the quadratic function to find the y-coordinate of the vertex. y = (5)^2 - 10(5) + 21 y = 25 - 50 + 21 y = -25 + 21 y = -4Determine Parabola Direction: Determine the direction of the parabola. Since the coefficient of x^2 (a = 1) is positive, the parabola opens upwards.Find Range: Find the range of the function. The vertex of the parabola is (5, -4), and since the parabola opens upwards, the y-values will be greater than or equal to the y-coordinate of the vertex. Range: {y | y ≥ -4}Match Range with Choices: Match the range with the given choices. The correct range is not listed in the choices provided. There seems to be an error in the choices, as none of them match the calculated range of {y | y ≥ -4}.

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What is the range of this quadratic function? $\newline$ $y = x^2 - 10x + 21$ $\newline$ Choices: $\newline$ (A) ${y | y \geq 5}$ $\newline$ (B) ${y | y \leq 5}$ $\newline$ (C) ${y | y \geq -4}$ $\newline$ (D)all real numbers

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Algebra 2

Domain and range of quadratic functions: equations

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Q. What is the range of this quadratic function?

\newline

y = x^2 - 10x + 21

\newline

Choices:

\newline

(A)

{y | y \geq 5}

\newline

(B)

{y | y \leq 5}

\newline

(C)

{y | y \geq -4}

\newline

(D)all real numbers

Identify Quadratic Function: Identify the quadratic function. $\newline$ We are given the quadratic function $y = x^2 - 10x + 21$ .
Find Vertex: Find the $x$ -coordinate of the vertex. $\newline$ To find the vertex of the parabola, we use the formula $x = -\frac{b}{2a}$ , where $a$ is the coefficient of $x^2$ and $b$ is the coefficient of $x$ . In this case, $a = 1$ and $b = -10$ . $\newline$ $x = -\frac{-10}{2 \cdot 1}$ $\newline$ $x = \frac{10}{2}$ $\newline$ $x = -\frac{b}{2a}$ $0$
Find Y-Coordinate: Find the y-coordinate of the vertex. $\newline$ Substitute $x = 5$ into the quadratic function to find the y-coordinate of the vertex. $\newline$ $y = (5)^2 - 10(5) + 21$ $\newline$ $y = 25 - 50 + 21$ $\newline$ $y = -25 + 21$ $\newline$ $y = -4$
Determine Parabola Direction: Determine the direction of the parabola. Since the coefficient of $x^2$ ( $a = 1$ ) is positive, the parabola opens upwards.
Find Range: Find the range of the function. $\newline$ The vertex of the parabola is $(5, -4)$ , and since the parabola opens upwards, the $y$ -values will be greater than or equal to the $y$ -coordinate of the vertex. $\newline$ Range: \{ $y | y \geq -4$ \}
Match Range with Choices: Match the range with the given choices. $\newline$ The correct range is not listed in the choices provided. There seems to be an error in the choices, as none of them match the calculated range of ${y | y \geq -4}$ .