Question

What is the vertex form of `y=x^2 +6x -3`?

Answer 1

To convert to vertex form, you must complete the square.

Explanation:

y = `x^2` + 6x - 3

y = 1(`x^2` + 6x + n) - 3

n = `(b/2)^2`

n = `(6/2)^2`

n = 9

y = 1(`x^2` + 6x + 9 - 9) - 3

y = 1(`x^2` + 6x + 9) -9 - 3

y = 1`(x + 3)^2` - 12

So, the vertex form of y = `x^2` + 6x - 3 is y = `(x + 3)^2` - 12.

Exercises:

1. Convert each quadratic function from standard form to vertex form:

a) y = `x^2` - 12x + 17

b) y = `-3x^2` + 18x - 14

c) y = `5x^2` - 11x - 19

1. Solve for x by completing the square. Leave any non-integer answers in radical form.

a) `2x^2` - 16x + 7 = 0

b) `3x^2` - 11x + 15 = 0

Good luck!