Question

Identify the vertex and axis of symmetry of 8xtle="y=-x^{2} +8x-12" alt="y=-x^{2} +8x-12" align="absmiddle" class="latex-formula">

Answer 1

$y=-x^2+8x-12\\y=-(x^2-8x)-12\\y=-[(x^2-8x+16)-16]-12\\y=-[(x-4)^2-16]-12\\y=-(x-4)^2+16-12\\y=-(x-4)^2+4$

Factor the minus or negative off the -x²+8x and don't do anything with -12

Find the number that can complete the square, for x²-8x, it'd be +16.

Just think of debt, you borrow, you have to give back. You borrow +16 then you have to give 16 out so you write -16 out of x²-8x+16 but still inside the bracket.

Distribute the minus/negative inside the bracket as you get -(x-4)²+16-12 because negative multiply negative and you get positive

Then you get y=-(x-4)^2+4

Because a<0, it's inverted parabola as shown below.

therefore, the vertex is at (4,4) or (-(-4), 4) because the vertex is at (-h,k) and h is -4 that means -h = 4

axis of symmetry is -b/2a, our b is 8, -b = -8 and 2a = 2(-1) so -8/-2 = 4 (From the standard form)

therefore, axis of symmetry is 4