Question

2. In factored form, a quadratic function can be written as y = (-2-x) (x-8). This parabola goes through the points (-2, 0) and (8, 0). Use your knowledge of the symmetry of the parabola to find the vertex. Show all work. 4 mark​

Answer 1

(3, 25)

Explanation:

The symmetry of a parabola means that if you have two y coordinates which are the same, the axis of symmetry is going to be in the middle of the x-coordinates. So in this case it's the middle number of -2 and 8. So to find the midpoint of these two numbers, you simply add them together and divide it by 2. This gives you the equation:
`(-2+8)/(2)=(6)/(2)=3`. This means that the axis of symmetry is at:
`x=3`, and as you may know, this axis of symmetry passes through the vertex. So this means the x-axis of the vertex is 3, so to find the y-value simply plug in 3 as x

y = (-2-3)(3-8)

y = (-5)(-5)

y = 25

So this means the vertex is at (3, 25)