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Step-by-step explanation:
f(x) = -16x² + 22x + 3
Factor:
f(x) = (8x + 1) (-2x + 3)
The x-intercepts are (-1/8, 0) and (3/2, 0).
The leading coefficient is negative, so the parabola points down. Therefore, the vertex is a maximum. The x-coordinate is halfway between the x-intercepts.
x = (-1/8 + 3/2) / 2
x = 11/16
f(11/16) = 169/16
So the vertex is at:
(11/16, 169/16)
Graph the x-intercepts and the vertex, then draw a curve through the 3 points.
