How do you find the vertex and the intercepts for #y=-2x^2 + 4x - 3#?
Vertex is (1, -1)
There are no real x-intercepts.
Y-intercepts are at (0, -3)
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
Since the discriminant is negative, it's context in the quadratic formula is
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.