Question

Micah found the vertex for the function y = -9.5x²-47.5x+63 as shown. Find and correct Micah's error.

x = -b/2a
x = -47.5/2(-9.5)
x = -47.5/-19
x = -(-2.5)
x = 2.5
y = -9.5(2.5)²-47.5(2.5)+63
y = -59.375-118.75+63
y = -115.125

Explain the erroг.

A. Micah used the wrong sign for b in the formula x = -b/2a
B. Micah should have found a positive value when he simplified the -9.5(2.5)² term
C. Micah did not use the correct order-of-operations dividing 47.5 by 2(-9.5).
D. Micah should have evaluated the function with x = 0 to find the y-coordinate.

Answer 1

Micah made an error in determining the sign of the x-coordinate while finding the vertex for the quadratic function. The correct x-coordinate of the vertex should be -2.5, not 2.5. The error corresponds to Micah using the wrong sign for the coefficient b in the vertex formula. Option number a is correct.

Step-by-step explanation:

The student Micah is attempting to find the vertex for the quadratic function y = -9.5x² - 47.5x + 63. The correct formula for the x-coordinate of the vertex is x = -b / (2a), where a and b are the coefficients from the quadratic equation in the form y = ax² + bx + c. Using this formula, Micah calculated the x-coordinate as:

x = -(-47.5) / (2 * -9.5)

x = 47.5 / -19

x = -2.5

Therefore, Micah made an error when determining the sign of the x-coordinate, as the final sign should be negative, not positive. This corresponds to error option A. Micah used the wrong sign for b in the formula x = -b / (2a). Additionally, the error in the evaluation of the function with x to find the y-coordinate suggests a potential miscalculation, but it is the sign of x that is the key issue.