What is the range of this quadratic function? y = x^2 - 4x + 4 Choices: (A){y | y ≥ 2} (B){y | y ≤ 0} (C){y | y ≥ 0} (D)all real numbers

Identify Quadratic Function: Identify the general form of the quadratic function. The given function is y = x^2 - 4x + 4, which is in the standard form y = ax^2 + bx + c, where a = 1, b = -4, and c = 4.Find Vertex X-coordinate: Find the x-coordinate of the vertex of the parabola. The x-coordinate of the vertex can be found using the formula x = -b/(2a). Substituting the values of a and b, we get: x = -(-4)/(2*1) = 4/2 = 2.Find Vertex Y-coordinate: Find the y-coordinate of the vertex by substituting the x-coordinate back into the original equation. Substitute x = 2 into y = x^2 - 4x + 4 to find the y-coordinate: y = (2)^2 - 4(2) + 4 = 4 - 8 + 4 = 0.Determine Parabola Direction: Determine the direction in which the parabola opens. Since the coefficient of x^2 (a = 1) is positive, the parabola opens upwards.Determine Range: Determine the range of the quadratic function. Given that the parabola opens upwards and the vertex is at (2, 0), the lowest point on the parabola is at y = 0. Therefore, the range of the function is all y-values greater than or equal to 0.

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What is the range of this quadratic function? $\newline$ $y = x^2 - 4x + 4$ $\newline$ Choices: $\newline$ (A) ${y | y \geq 2}$ $\newline$ (B) ${y | y \leq 0}$ $\newline$ (C) ${y | y \geq 0}$ $\newline$ (D)all real numbers

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Algebra 1

Domain and range of quadratic functions: equations

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Q. What is the range of this quadratic function?

\newline

y = x^2 - 4x + 4

\newline

Choices:

\newline

(A)

{y | y \geq 2}

\newline

(B)

{y | y \leq 0}

\newline

(C)

{y | y \geq 0}

\newline

(D)all real numbers

Identify Quadratic Function: Identify the general form of the quadratic function. $\newline$ The given function is $y = x^2 - 4x + 4$ , which is in the standard form $y = ax^2 + bx + c$ , where $a = 1$ , $b = -4$ , and $c = 4$ .
Find Vertex X-coordinate: Find the x-coordinate of the vertex of the parabola. $\newline$ The x-coordinate of the vertex can be found using the formula $x = -\frac{b}{2a}$ . Substituting the values of $a$ and $b$ , we get: $\newline$ $x = -\frac{-4}{2\cdot 1} = \frac{4}{2} = 2$ .
Find Vertex Y-coordinate: Find the y-coordinate of the vertex by substituting the x-coordinate back into the original equation. $\newline$ Substitute $x = 2$ into $y = x^2 - 4x + 4$ to find the y-coordinate: $\newline$ $y = (2)^2 - 4(2) + 4 = 4 - 8 + 4 = 0$ .
Determine Parabola Direction: Determine the direction in which the parabola opens. $\newline$ Since the coefficient of $x^2$ ( $a = 1$ ) is positive, the parabola opens upwards.
Determine Range: Determine the range of the quadratic function. $\newline$ Given that the parabola opens upwards and the vertex is at $(2, 0)$ , the lowest point on the parabola is at $y = 0$ . Therefore, the range of the function is all $y$ -values greater than or equal to $0$ .