Question

How do I convert y = a(x –7)^2 + 28 into standard form?

Answer 1

Step #1 you need to expand that (x-7)^2 and foil it you know how to do that?

\[a(x-7)(x-7)+28 \]

Answer 2

Please expand (x-7)^2, and then mult. each term of the result by the coefficient a.

Answer 3

Thus: a(x-7)^2=a(x^2 - ???? ) +28

Answer 4

\[(x ^{2} +7x+ 7x+ 14) + 28\]

Answer 5

Wouldn't each "7x" actually be "-7x?" Where did that +14 come from? (Hint: What's 7^2)?)

Answer 6

I foiled a(x−7)(x−7)+28

Answer 7

@mathmale

Answer 8

(x^2-7x-7x+49)+28

Answer 9

Much better. Combining terms: x^2 - 14x + 49 +28 = ??

Answer 10

14x^3+77

Answer 11

We must keep the powers of x separate. x^2 - 14x cannot be combined.

The correct result would be x^2 - 14x + 77.

Answer 12

I thought so but I wasn't sure so I just combined them.

Answer 13

So is x^2 - 14x + 77 standard form of y=a(x-7)^2+28?

Answer 14

Originally you had y = a(x-7)^2+28. We can't just forget about the 'a." So now we have to figure out how to include the 'a' in your final equation.

You could begin with your intermediate result, x^2 - 14x + 49 (no 28) and mult. each of these three terms by 'a.' This would end with 49a, which can't be combined with 28 except by writing "49a+28."

Answer 15

so 49a + 28 is the final answer ?

Answer 16

@Satellite73

Answer 17

>>so 49a + 28 is the final answer ? No.

Answer 18

I'm confused so what do I do do I times (x^2 - 14x + 49) (49a +28)

Answer 19

y = a * ( x^2 - 49x + 49 ) + 28

To this point is correct.

Answer 20

Distribute (multiply) the "a" times this: ( x^2 - 49x + 49 ). Do not multiply a times the 28. It is not inside the parentheses with the other terms.

Answer 21

>>I times (x^2 - 14x + 49) (49a +28) No

Answer 22

y = a * ( x^2 - 49x + 49 ) + 28 so this would be the correct answer or would I need to multiply this?

Answer 23

What is a times 49 =