# How do you find the vertex and the intercepts for #y=-2x^2 + 4x - 3#?

##### 1 Answer

Vertex is (1, -1)

There are no real x-intercepts.

Y-intercepts are at (0, -3)

#### Explanation:

First, using

The x-coordinate of the vertex is found by calculating

Now, we plug in

So we can reasonably conclude that the vertex is the point (1, -1). In order to find the x-intercepts, it is the values of

I'll save you the time, the polynomial does not factor easy. So we can then use the quadratic equation to calculate the values of *discriminant*, which reveals what types of roots the equation has.

Since the discriminant is negative, it's context in the quadratic formula is *no real roots*, or no real x-intercepts.

On another note, let's go to the y-intercept(s). We can say that the graph intercepts the y-axis where

With this, we can say (0, -3) is a point and that it is the only y-intercept of the equation.