Question

How do you find the important points to graph `f(x)= -2x^2 + 3x +1`?

Answer 1

f(x ) = -2x^2 + 3x + 1

Explanation:

Important points to graph f(x)
1. Vertex.
x-coordinate of vertex:`x = -b/(2a) = -3/-4 = 3/4`
y-coordinate of vertex:
`f(3/4) = -2(9/16) + 3(3/4) + 1 = -18/16 + 9/4 + 1 = 17/8`
Vertex (3/4, 17/8)
2. y-intercept
To find y-intercept, make x = 0 --> y = 1
3. x-intercepts.
To find x-intercepts, make f(x) = 0 and solve the quadratic equation: `y = -2x^2 + 3x + 1 = 0.`
`D = d^2 = b^2 - 4ac = 9 + 8 = 17` --> `d = +- sqrt17`
`x = 3/4 +- (sqrt17)/4 = (3 +- sqrt17)/4`
graph{-2x^2 + 3x + 1 [-10, 10, -5, 5]}