Answer:
y = x^2 + 6x +7
y=-x+1
Explanation:
To answer this question, we need to find the equation for the line and for the parabola. So, let's do just that!
Line:
The line has a slope of -1 and and y-intercept of 1. This means that the equation for the line is y=-x+1.
Parabola:
To find the vertex form of a parabola, we must first find the vertex form of a parabola. The vertex form of a parabola is y=a(x-h)^2+k, where the vertex is (h,k). Since the vertex of the parabola is (-3,-2), h=-3 and k=-2. Let's plug these values into the vertex form of a parabola.
y=a(x-h)^2+k
y=a(x-(-3))^2+(-2)
y=a(x+3)^2-2
We're not done yet, though, as we still need to find the value of a. To do this, we will take one of the points on the parabola and plug it into the equation. I will be using the point (-1,2).
y=a(x+3)^2-2 [Plug in x and y values]
2=a((-1)+3)^2-2 [Simplify]
2=a(2)^2-2 [Simplify]
2=4a-2 [Add 2 to both sides]
4=4a [Divide both sides by 4]
a=1
Now, we know that the equation of our parabola in vertex form is y=(x+3)^2-2. This isn't what the problem is asking for, though. Instead, they want the standard form of the parabola. To do this, we will need to expand y=(x+3)^2-2.
y=(x+3)^2-2
y=x^2 + 6x + 9 -2
y = x^2 + 6x +7
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