Answer:
y = 3(x - 4)² - 38
Step-by-step explanation:
We need to complete the square on
y = 3(x² - 8x) + 10
A quadratic equation is in the form of y = ax² + bx + c. To complete the square, take half of the b term (here, the b term is -8), then square it...
-8/2 = -4
(-4)² = 16
Now add and subtract that from the equation...
y = 3(x² - 8x + 16 - 16) + 10
Now pull out the -16 from the parenthesis, be careful though, there is a multiplier of 3 in front of the parenthesis, so it come out as a positive -48
y = 3(x² - 8x + 16) + 10 - 48
x² - 8x + 16 is a perfect square trinomial (we did this by completing the square), so it factors to (x - 4)², and 10 - 48 = -38, so our equation becomes...
y = 3(x - 4)² - 38
This is now in vertex form, which is either the minimum or maximum.
Vertex form is
y = a(x - h)² + k, where (h, k) is the vertex. If a > 0, then the vertex is a minimum, if a < 0, then the vertex is a maximum.
Our vertex is (4, -38)
