What is the range of this quadratic function? y = x^2 + 2x - 15 Choices: (A){y | y ≥ -16} (B){y | y ≤ -16} (C){y | y ≥ -1} (D)all real numbers

Identify Quadratic Function: Identify the quadratic function and its coefficients. The given quadratic function is y = x^2 + 2x - 15. The coefficients are a = 1, b = 2, and c = -15.Find Vertex x-coordinate: Find the x-coordinate of the vertex. The x-coordinate of the vertex of a parabola given by y = ax^2 + bx + c is found using the formula x = -b/(2a). Here, a = 1 and b = 2. x = -2/(2*1) x = -2/2 x = -1Find Vertex y-coordinate: Find the y-coordinate of the vertex by substituting x = -1 into the quadratic function. y = (-1)^2 + 2(-1) - 15 y = 1 - 2 - 15 y = -16Determine 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 (-1, -16), 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 ≥ -16}

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What is the range of this quadratic function? $\newline$ $y = x^2 + 2x - 15$ $\newline$ Choices: $\newline$ (A) ${y | y \geq -16}$ $\newline$ (B) ${y | y \leq -16}$ $\newline$ (C) ${y | y \geq -1}$ $\newline$ (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 + 2x - 15

\newline

Choices:

\newline

(A)

{y | y \geq -16}

\newline

(B)

{y | y \leq -16}

\newline

(C)

{y | y \geq -1}

\newline

(D)all real numbers

Identify Quadratic Function: Identify the quadratic function and its coefficients. $\newline$ The given quadratic function is $y = x^2 + 2x - 15$ . The coefficients are $a = 1$ , $b = 2$ , and $c = -15$ .
Find Vertex x-coordinate: Find the x-coordinate of the vertex. $\newline$ The x-coordinate of the vertex of a parabola given by $y = ax^2 + bx + c$ is found using the formula $x = -\frac{b}{2a}$ . Here, $a = 1$ and $b = 2$ . $\newline$ $x = -\frac{2}{2\cdot 1}$ $\newline$ $x = -\frac{2}{2}$ $\newline$ $x = -1$
Find Vertex y-coordinate: Find the y-coordinate of the vertex by substituting $x = -1$ into the quadratic function. $y = (-1)^2 + 2(-1) - 15$ $y = 1 - 2 - 15$ $y = -16$
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 $(-1, -16)$ , and since the parabola opens upwards, the $y$ -values will be greater than or equal to the $y$ -coordinate of the vertex. $\newline$ Range: \{ $y | y \geq -16$ \}