Question

Use the method of completing the square to write the equations of the given parabola in this form:

(y-k)=a(x-h)^2
where a =0, (h,k) is the vertex, and x=h is the axis of symmetry.
Find the vertex of this parabola: y=-4x^2+8x-12

Answer 1

The vertex is the point (1,-8)

Explanation:

we have

`y=-4x^(2) +8x-12`

Convert to vertex form

step 1

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`y+12=-4x^(2) +8x`

step 2

Factor the leading coefficient

factor -4

`y+12=-4(x^(2) -2x)`

step 2

Complete the square. Remember to balance the equation by adding the same constants to each side

`y+12-4=-4(x^(2) -2x+1)`

`y+8=-4(x^(2) -2x+1)`

step 3

Rewrite as perfect squares

`y+8=-4(x-1)^(2)`

therefore

The vertex is the point (1,-8)