domain and range

Question

domain and range of y=-2x²-5x+7

Answer 1

The domain is the whole real line.

The range is (-∞,10.125).

The maximum occurs at x=-5/4 and the max value is 10.125)

Answer 2

y = -2x² -5x + 7

Where:

a = -2

b= -5

c= 7

Domain of a parabola: All Real numbers

Domain: - ∞ ≤ x ≤ + ∞

Range of a parabola. Find its Vertex: (x_v , y_v)

x_v = -b / 2a

x_v = -(-5) / 2(-2)

x_v = 5 / -4

x_v = - 5/4

y_v = f(-5/4)

y_v = -2(-5/4)² - 5(-5/4) + 7

y_v = -2(25/16) + 25/4 + 7

y_v = -50/16 + 25/4 + 7

y_v = 81/8

Vertex: (-5/4, 81/8)

Since a = -2 < 0 → The parabola has a Maximum value at y = 81/8

Range: y ≤ 81/8