How do you find the vertex and the intercepts for F(x)=x^2-4x-7?

Mar 21, 2016

Vertex is (2, $-$11). y-intercept is $- 7$, This parabola cuts x-axis at $\left(2 \pm \sqrt{11} , 0\right)$. The length in-between is 2$\sqrt{11}$. .

Explanation:

The equation has the form ${\left(x - 2\right)}^{2} = y + 11$.

This represents the parabola with vertex at (2, $-$11).

The axis of the parabola is the line x = 2, from the vertex in the positive direction of the y-axis.

To get intercept on the x-axis, put y = 0 in the equation and find x.

For the y-intercept put xo 0.,