What is the range of this quadratic function? y = x^2 + 2x - 35 Choices: (A){y | y ≤ -1} (B){y | y ≥ -1} (C){y | y ≥ -36} (D)all real numbers

Find Vertex: We have the quadratic function y = x^2 + 2x - 35. To find the range, we need to determine the vertex of the parabola. The x-coordinate of the vertex is given by x = -b/(2a). In our case, a = 1 and b = 2. So, x = -2/(2*1) = -2/2 = -1.Calculate Vertex Coordinates: Now we need to find the y-coordinate of the vertex by substituting x = -1 into the equation y = x^2 + 2x - 35. y = (-1)^2 + 2(-1) - 35 = 1 - 2 - 35 = -36. So, the vertex of the parabola is at the point (-1, -36).Determine Parabola Direction: Since the coefficient of x^2 is positive (a = 1), the parabola opens upwards. This means that the vertex represents the minimum point on the graph of the quadratic function.Identify Range: The range of the function is all the y-values that the function can take. Since the parabola opens upwards and the vertex is the lowest point, the range is all y-values greater than or equal to the y-coordinate of the vertex. Therefore, the range is {y | y ≥ -36}.

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What is the range of this quadratic function? $\newline$ $y = x^2 + 2x - 35$ $\newline$ Choices: $\newline$ (A) $\{y | y \leq -1\}$ $\newline$ (B) $\{y | y \geq -1\}$ $\newline$ (C) $\{y | y \geq -36\}$ $\newline$ (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 - 35

\newline

Choices:

\newline

(A)

\{y | y \leq -1\}

\newline

(B)

\{y | y \geq -1\}

\newline

(C)

\{y | y \geq -36\}

\newline

(D)all real numbers

Find Vertex: We have the quadratic function $y = x^2 + 2x - 35$ . To find the range, we need to determine the vertex of the parabola. $\newline$ The x-coordinate of the vertex is given by $x = -\frac{b}{2a}$ . In our case, $a = 1$ and $b = 2$ . $\newline$ So, $x = -\frac{2}{2\cdot1} = -\frac{2}{2} = -1$ .
Calculate Vertex Coordinates: Now we need to find the y-coordinate of the vertex by substituting $x = -1$ into the equation $y = x^2 + 2x - 35$ . $y = (-1)^2 + 2(-1) - 35 = 1 - 2 - 35 = -36$ .So, the vertex of the parabola is at the point $(-1, -36)$ .
Determine Parabola Direction: Since the coefficient of $x^2$ is positive ( $a = 1$ ), the parabola opens upwards. This means that the vertex represents the minimum point on the graph of the quadratic function.
Identify Range: The range of the function is all the y-values that the function can take. Since the parabola opens upwards and the vertex is the lowest point, the range is all y-values greater than or equal to the y-coordinate of the vertex. $\newline$ Therefore, the range is ${y | y \geq -36}$ .