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Shtirlitz [24]
3 years ago
9

Need 2 more. 50 points! Please show work, Thanks! :)

Mathematics
1 answer:
rjkz [21]3 years ago
3 0

Answer:

1) C

2) C

Step-by-step explanation:

Question 1)

We want a parabola that has the vertex (-8, -7) and also passes through the point (-7, -4).

So, we can use the vertex form. Remember that the vertex form is:

y=a(x-h)^2+k

Where a is our leading co-efficient and (h, k) is our vertex.

We know that our vertex is (-8, -7). So, substitute this into the equation:

y=a(x-(-8))^2+(-7)

Simplify:

y=a(x+8)^2-7

Now, we need to determine the value of our a. To do so, we can use the point the problem had given us. We know that the graph passes through (-7, -4).

So, when x is -7, y is -4. Substitute -7 for x and -4 for y:

(-4)=a((-7)+8)^2-7

Solve for a. Add within the parentheses:

-4=a(1)^2-7

Square:

-4=a-7

Add 7 to both sides. Therefore, the value of a is:

a=3

So, our entire equation in vertex form is:

y=3(x+8)^2-7

Our answer is C.

Question 2)

We are given a graph and are asked to find the equation of the graph.

Again, let's use the vertex form. From the graph, we can see that the vertex is at (-2, 2). Let's substitute this into our vertex equation:

y=a(x-(-2))^2+2

Simplify:

y=a(x+2)^2+2

Again, we need to find the value of a.

Notice that the graph crosses the point (-1, 5).

So, let's substitute -1 for x and 5 for y. This yields:

5=a((-1)+2)^2+2

Solve for a. Add within the parentheses.

5=a(1)^2+2

Square:

5=a+2

Subtract 2 from both sides. So, the value of a is:

a=3

Therefore, our entire equation is:

y=3(x+2)^2-2

Our answer is C.

And we're done!

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