Answer:
y = 2(x - 5)² - 3
Step-by-step explanation:
The vertex of a quadratic equation in the following format:
y = ax² + bx + c
Is the point (xv,yv), in which
[tex]x_V=-\frac{b}{2a}[/tex][tex]y_V=-\frac{b^2-4ac}{4a}[/tex]
The equation of the parabola in vertex form is given by:
[tex]y=a(x-x_V)^2+y_V[/tex]
In this question:
y = 2x² - 20x + 47
So a = 2, b = -20, c = 47
[tex]x_V=-\frac{b}{2a}=-\frac{-20}{2\ast2}=-(-5)=5[/tex][tex]y_V=-\frac{(-20)^2-4\ast2\ast47}{4\ast2}=-\frac{400-376}{8}=-3[/tex]
So the vertex form of the quadratic equation is:
y = 2(x - 5)² - 3
