Question

What is the equation of the graph below? A graph shows a parabola that opens up and crosses the x axis at negative two and negative four.

Answer 1

y = a(x-h)2+k. (h,k) is the equation for the parabola
Plug the values in with the variables
You will get your right answer

Answer 2

The function of a parabola is y= ax² + b x c

If x' = -2 & x" = - 4 are the x intercepts then x= - 2 & x"= - 4 are the roots of this quadratic equation, we also know that this equation can be written as:

x² - Sx +P, where S= x' + x" (sum) & P = x' . x" (product), also we know (given) that x' = -2 & x" = - 4, hence, plug fpr S & P

x² - (-6) x + 8

===.> Y= X²+6X+8

& ITS AXIS OF SYMMETRY (-b/2a)  ===> x= -3.

a is positive so it passes by a minimum (open up) Minimum (-3,-1)