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 quadratic function and its coefficients. The given quadratic function is y = x^2 + 4x + 4. Here, the coefficients are 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) x = -4/2 x = -2Find Vertex y-coordinate: Find the y-coordinate of the vertex by substituting the x-coordinate into the original equation. Substitute x = -2 into y = x^2 + 4x + 4 to find the y-coordinate of the vertex: y = (-2)^2 + 4(-2) + 4 y = 4 - 8 + 4 y = 0Determine Parabola Direction: Determine the direction in which the parabola opens. Since the coefficient a = 1 is positive, the parabola opens upwards.Find Range: Find the range of the quadratic function. The vertex of the parabola is (-2, 0), and since the parabola opens upwards, the range of the function is all y-values greater than or equal to the y-coordinate of the vertex. Range: {y | y ≥ 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 quadratic function and its coefficients. $\newline$ The given quadratic function is $y = x^2 + 4x + 4$ . Here, the coefficients are $a = 1$ , $b = 4$ , 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: $\newline$ $x = -\frac{4}{2 \times 1}$ $\newline$ $x = -\frac{4}{2}$ $\newline$ $x = -2$
Find Vertex y-coordinate: Find the y-coordinate of the vertex by substituting the x-coordinate into the original equation. $\newline$ Substitute $x = -2$ into $y = x^2 + 4x + 4$ to find the y-coordinate of the vertex: $\newline$ $y = (-2)^2 + 4(-2) + 4$ $\newline$ $y = 4 - 8 + 4$ $\newline$ $y = 0$
Determine Parabola Direction: Determine the direction in which the parabola opens. $\newline$ Since the coefficient $a = 1$ is positive, the parabola opens upwards.
Find Range: Find the range of the quadratic function. $\newline$ The vertex of the parabola is $(-2, 0)$ , and since the parabola opens upwards, the range of the function is all $y$ -values greater than or equal to the $y$ -coordinate of the vertex. $\newline$ Range: \{ $y | y \geq 0$ \}