Question

How do you find the vertex and intercepts for `f(x) = -5x^2 + 7x + 4`?

Answer 1

Find vertex and intercepts of f(x) = - 5x^2 + 7x + 4

Explanation:

x-coordinate of vertex:
`x = (-b)/(2a) = 7/10`
y-coordinate of vertex:
`y = f(7/10) = - 49/100 + 49/10 + 4 = 645/100`
To find y-intercept, make x = 0 --> f(x) = 4
To find x-intercepts, make y = 0 and solve the quadratic equation:
`-5x^2 + 7x + 4 = 0`.
`D = d^2 = b^2 - 4ac = 49 + 80 = 129` --> `d = +- sqrt29 = +- 5.39`
`x = -7/10 +- 5.39/10 = - 0.7 - 5.39 = -6.09` and
`x = -7/10 + 5.39 = 5.39 - 0.7 = 4.69`