Question

How do you find the vertex and intercepts for `f(x)=12.25x^2 - 52.5x +110.25`?

Answer 1

Vertex (2.14, 54)

Explanation:

`f(x) = 12.25x^2 - 52.5x + 110.25`
x-coordinate of vertex:
`x = -b/(2a) = 52.5/24.5 = 2.14`
y-coordinate of vertex:
`f(2.14) = 12.25(2.14)^2 - 52.5(2.14) + 110.25 =`
`= 56.1 - 112.35 + 110.25 = 54`
Vertex (2.14, 54)
To find the 2 intercepts, solve the quadratic equation:
`f(x) = 12.25x^2 - 52.5x + 110.25 = 0`
`D = d^2 = b^2 - 4ac = 2756.25 - 5402.25 = - 2646 < 0`
Since D < 0, there are no x-intercepts. The parabola graph of f(x)
stays completely above the x-axis.