Question

Can someone help confirm my work?

f(x) = 4x2 − 7x − 15

Part A Finding X-intercepts:
f(x) = 4x^2 − 7x − 15
0 = 4x^2 − 7x − 15
a = 4, b = -7, c= -15
a * c = -60
-12 * 5 = -60
-12 + 5 = -7
(4x + 5)(4x -12)
4x^2 - 12x | + 5x -15
4x(x - 3) + 5(x - 3)
(x - 3)(4x +5)
x = 3 x = -1.25 or -5/4

Part B Finding Vertex:
minimum point
(x1 + x2)/2
(3 -1.25)/2 = 0.875
f(x) = 4x^2 − 7x − 15
f(0.875) = 4(0.875)^2 − 7(0.875) − 15
f(0.875) = 3.06 - 6.125 - 15
f(0.875) = -18.065

vertex = (0.875, -18.065)

Answer 1

You have the intercepts and x-coordinate of the vertex correct. There appears to be a math error in the calculation of the y-value of the vertex.

f(7/8) = (4*7/8 -7)*(7/8) -15 = -49/16 -15 = -289/16 = -18.0625