Question

How do you write `f(x)= -x^2 + 3x + 10` in vertex form and identify the vertex, y intercept and x intercept?

Answer 1

`f(x) = -x^2 + 3x + 10`

Explanation:

x-cordinate of vertex: `x = (-b/2a) = -3/-2 = 3/2`
y-coordinate of vertex: `y = f(3/2) = - 9/4 + 9/2 + 10 = 49/4`

Vertex form: `f(x) = -(x - 3/2)^2 + 49/4`
To find y-intercept, make x = 0 --> y = 10
To find x-intercepts, solve f(x) = 0.
Find 2 numbers knowing sum (-3) and product (-10).
The 2 real roots (x-intercepts) are: -2 and 5.