Question

Which is the vertex form of the equation for the quadratic function y = 2x2 - 20x +47?

Answer 1

y = 2(x - 5)² - 3

Explanation:

The vertex of a quadratic equation in the following format:

y = ax² + bx + c

Is the point (xv,yv), in which

`x_V=-(b)/(2a)`
`y_V=-(b^2-4ac)/(4a)`

The equation of the parabola in vertex form is given by:

`y=a(x-x_V)^2+y_V`

In this question:

y = 2x² - 20x + 47

So a = 2, b = -20, c = 47

`x_V=-(b)/(2a)=-(-20)/(2\ast2)=-(-5)=5`
`y_V=-((-20)^2-4\ast2\ast47)/(4\ast2)=-(400-376)/(8)=-3`

So the vertex form of the quadratic equation is:

y = 2(x - 5)² - 3