pleaseeee helpp!1

Question

y=5x^2 + 20x - 6 Into y = a (x-p)^2 + q

Answer 1

Completing the square Method :

The expression is y = 5x² + 20x - 6.

Take out common factor.

y = 5(x² + 4x - 6/5)

To change the expression (x² + 4x) into a perfect square trinomial add (half the x coefficient)² to each side of the expression.

 Here x coefficient = 4. So, (half the x coefficient)² = (4/2)² = 4.

Add and subtract 4 to the expression.

y = 5(x² + 4x - 6/5 + 4 - 4)

y = 5(x² + 4x + 4 - 6/5 - 4)

y = 5(x² + 4x + 4 - 26/5)

y = 5(x² + 2(2)(x) + 2²) - 26

Apply Perfect Square Trinomial : u² + 2uv + v² = (u + v)².

y = 5(x + 2)² - 26

The solution is y = 5[x - (- 2)]² + (- 26).

Now it is in the form of y = a(x - p)² + q.

a = 5, p = - 2 and q = - 26.