How do you find the vertex and intercepts for #y = - 2x^2 + 8x + 4#?
The x-intercepts are simply the roots of the quadratic,
The y-intercept is simply the constant term,
The vertex is the point at which the slope (gradient) is zero, so differentiate and then solve to find the point
I'll use the method that requires calculus. Another answerer may be able to answer using only algebra.
First visualise the curve: the
The x-intercepts occur when
Solve using the quadratic formula or otherwise:
To find the vertex, we know that it is a point where the gradient =
Set this equal to zero:
Therefore the coordinates of the vertex are