Rewrite each function in the form y = a(x-h)^2-k. Find each vertex.
y = x^2 -8x + 18
y = (x - 4)^2-2
y = x^2 -8x + 16 +2
= (x-4)^2 + 2
= (x-4)^2 - (-2)
The vertex would be x=4, y = 2
To rewrite the given quadratic function in the form y = a(x-h)^2-k, we need to complete the square.
Step 1: Group the x-terms together.
y = (x^2 - 8x) + 18
Step 2: Take half of the coefficient of x (-8) and square it to find the constant that completes the square. In this case, (-8/2)^2 = 16.
y = (x^2 - 8x + 16) - 16 + 18
Step 3: Rewrite the expression inside the parentheses as a perfect square trinomial.
y = (x - 4)^2 - 16 + 18
Step 4: Simplify the constants.
y = (x - 4)^2 + 2
Now we have rewritten the function in the desired form. The vertex of the parabola can be identified by comparing the equation with y = a(x - h)^2 - k.
From the rewritten equation, we can see that the vertex is (h, k) = (4, 2). So, the vertex of the parabola is at point (4, 2).