Question

How to transform this to vertex form 2x^2-18x+8

Answer 1

Answer:

see explanation

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square

• The coefficient of the x² term must be 1

y = 2(x² - 9x) + 8

• add/subtract (half the coefficient of the x- term)² to x² - 9x

y = 2(x² + 2 (- $\frac{9}{2}$) x + (- $\frac{9}{2}$)² - (- $\frac{9}{2}$)²) + 8

y = 2(x - $\frac{9}{2}$)² - 2($\frac{81}{4}$ + 8

  = 2(x - $\frac{9}{2}$)² - $\frac{65}{2}$ ← in vertex form