Question

Rewrite the equation y=x^2−5x−6 in factored form and find the zeros of the equation. Then use the zeros to find the line of symmetry of the parabola represented by the equation.

What is the equation for the line of symmetry of the parabola represented by the equation y=x^2−5x−6?

x=−2.5
x=2.5
x=0.5
x=−3.5
x=3.5
x=−0.5

Answer 1

Hi there!

`\large\boxed{x = 2.5}`

y = x² - 5x - 6

Rewrite into factored form by finding two numbers that sum up to -5 and multiply into -6. We can use the numbers -6 and 1:

y = (x - 6)(x + 1) is the equation in factored form.

There are zeroes at:

0 = x - 6

x = 6

0 = x + 1

x = -1

Find the x-value exactly half-way between the two zeroes to find the axis of symmetry:

(-1 + 6) / 2 = 5 / 2 = 2.5

Therefore, the equation for the line of symmetry is:

x = 2.5