Question

Put the quadratic into vertex form and state the coordinates of the vertex
y=x^2-6x+7
Vertex form:y=___________
Vertex:(,)

Answer 1

To put the quadratic equation y = x^2 - 6x + 7 into vertex form, we can complete the square.

First, let's rewrite the equation by grouping the x terms:
y = (x^2 - 6x) + 7

Now, we need to add and subtract the square of half the coefficient of x (which is (-6/2)^2 = 9) within the parentheses:
y = (x^2 - 6x + 9 - 9) + 7

Simplify this equation:
y = (x^2 - 6x + 9) - 9 + 7
y = (x - 3)^2 - 2

Therefore, the quadratic equation y = x^2 - 6x + 7 can be written in vertex form as y = (x - 3)^2 - 2.

The coordinates of the vertex are (3, -2).