By solving a system of equations we will see that the equation is:
y = x^2 + 6*x + 8
How to find the equation of a parabola?
A quadratic equation is written as:
y = a*x^2 + b*x + c
First, the value of c is the value that takes the function when x = 0, this is the y-intercept, by looking at the image we can see that it intercepts the y-axis at:
y = 8 = c.
Then our equation is:
y = a*x^2 + b*x + 8
Now we need to find the values of a and b.
In the graph we can also see that:
x = -4 and x = -2 are roots of the equation, this means that:
0 = a*(-4)^2 + b*(-4) + 8
0 = a*(-2)^2 + b*(-2) + 8
This is a system of equations:
0 = 16*a - 4*b + 8
0 = 4*a - 2*b + 8
In the second equation we can isolate b, we will get:
b = (4*a + 8)/2 = 2*a + 4
We can replace that in the other equation to get:
0 = 16*a - 4*(2*a + 4) + 8
0 = 16*a - 8*a - 16 + 8
0 = 8*a - 8
a = 8/8 = 1
Now that we know the value of a, we can use the equation:
b = 2*a + 4 = 2*1 + 4 = 6
Then the quadratic equation is:
y = x^2 + 6*x + 8
If you want to learn more about parabolas, you can read:
https://brainly.com/question/1480401
