Identify the coefficient of the x2 term.

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Here's the solution for the given function f(x) = −x² − 2x + 24. a) Will the function have a minimum or maximum? Step 1: Identify the coefficient of the x² term. For the function f(x) = −x² − 2x + 24, the coefficient of x² is a = −1. Step 2: Determine if the parabola opens upwards or downwards. Since a = −1 is negative (a < 0), the parabola opens downwards. Step 3: Conclude whether it's a minimum or maximum. A parabola that opens downwards has a highest point, which is a maximum. The function will have a maximum. b) Determine the x-coordinates of the turning point. Step 1: Use the formula for the x-coordinate of the turning point (vertex) of a parabola f(x) = ax² + bx + c. The formula is x = −b/2a. From the function f(x) = −x² − 2x + 24, we have a = −1 and b = −2. Step 2: Substitute the values of a and b into the formula. x = −(−2)/(2(−1)); x = −(−2)/(−2); x = −(1); x = −1 The x-coordinate of the turning point is −1. c) Determine the y-coordinates of the turning point. Step 1: Substitute the x-coordinate found in part b) into the original function f(x). We found x = −1. f(x) = −x² − 2x + 24; f(−1) = −(−1)² − 2(−1) + 24 Step 2: Calculate the value of f(−1). f(−1) = −(1) + 2 + 24; f(−1) = −1 + 2 + 24; f(−1) = 1 + 24; f(−1) = 25 The y-coordinate of the turning point is 25.

Identify the coefficient of the x2 term.

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Step-by-step solution

Part a· 3 steps