What is the range of this quadratic function? y = x^2 - 12x + 35 Choices: (A){y | y ≥ 6} (B){y | y ≥ -1} (C){y | y ≤ -1} (D)all real numbers

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What is the range of this quadratic function?   y = x^2 - 12x + 35    Choices: (A){y | y ≥ 6} (B){y | y ≥ -1} (C){y | y ≤ -1} (D)all real numbers

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Find Vertex: We have the quadratic function y = x^2 - 12x + 35. To find the range, we first need to determine the vertex of the parabola. The x-coordinate of the vertex can be found using the formula x = -b/(2a), where a is the coefficient of x^2 and b is the coefficient of x.Calculate x-coordinate: Substitute a = 1 and b = -12 into the formula x = -b/(2a) to find the x-coordinate of the vertex. x = -(-12)/(2*1) x = 12/2 x = 6Calculate y-coordinate: Now that we have the x-coordinate of the vertex, we can find the y-coordinate by substituting x = 6 into the original equation y = x^2 - 12x + 35. y = (6)^2 - 12(6) + 35 y = 36 - 72 + 35 y = -36 + 35 y = -1Determine Parabola Direction: The vertex of the parabola is (6, -1). 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.Find Range: Given that the parabola opens upwards and the y-coordinate of the vertex is -1, the range of the function is all y-values that are greater than or equal to -1. Range: {y | y ≥ -1}

What is the range of this quadratic function? $\newline$ $y = x^2 - 12x + 35$ $\newline$ Choices: $\newline$ (A) ${y | y \geq 6}$ $\newline$ (B) ${y | y \geq -1}$ $\newline$ (C) ${y | y \leq -1}$ $\newline$ (D)all real numbers

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What is the range of this quadratic function?\newliney=x2−12x+35y = x^2 - 12x + 35y=x2−12x+35\newlineChoices:\newline(A)y∣y≥6{y | y \geq 6}y∣y≥6\newline(B)y∣y≥−1{y | y \geq -1}y∣y≥−1\newline(C)y∣y≤−1{y | y \leq -1}y∣y≤−1\newline(D)all real numbers

What is the range of this quadratic function? $\newline$ $y = x^2 - 12x + 35$ $\newline$ Choices: $\newline$ (A) ${y | y \geq 6}$ $\newline$ (B) ${y | y \geq -1}$ $\newline$ (C) ${y | y \leq -1}$ $\newline$ (D)all real numbers