Question

Express the following quadratic function in vertex form. F(x)=-2x^2+x-2

Answer 1

f(x) = - 2(x - $\frac{1}{4}$)² - $\frac{15}{8}$

the equation of a quadratic 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 , factor out - 2

= - 2(x² - $\frac{1}{2}$x) - 2

• add / subtract (half the coefficient of the x-term )² to x² - $\frac{1}{2}$x

= - 2(x² + 2(- $\frac{1}{4}$)x + $\frac{1}{16}$ - $\frac{1}{16}$) - 2

= - 2(x - $\frac{1}{4}$)² + $\frac{1}{8}$ - 2

= - 2(x - $\frac{1}{4}$)² - $\frac{15}{8}$