How do you find the vertex and intercepts for f(x)=10x25x+12?

1 Answer
Jun 28, 2018

Vertex (14,918)
No x-intercepts

Explanation:

f(x)=10x25x+12
x - coordinate of vertex:
x=b2a=520=14
y-coordinate of vertex:
f(14)=10(116)5(14)+12=58108+968=918
Vertex (14,918)
y-intercept when x = 0, --> f(0) = 12
x- intercepts when f(x) = 0. Solve the quadratic equation:
f(x)=10x25x+12=0
D=d2=b24ac=25480=455<0.
There are no x-intercepts. The graph of f(x) is an upward parabola (a > 0), that completely stays above the x-axis.