Question

Write the following quadratic function in vertex form. Determine the vertex and the axis of symmetry for the function f(x)=-5x^2+7x+9

Answer 1

Have you considered "Completing the Square"?

Answer 2

Yes, I always get messed up and I just can't complete the square. It's been something I've been trying to work on..

Answer 3

Well, let's walk through it. First, you have to get this burned into your brain: \((a+b)^{2} = a^{2} + 2ab + b^{2}\) Stare at the 'b'-parts.

Answer 4

Okay, now what?

Answer 5

There are a few ways to go about it, bu I like to make the leading coefficient one (1).
f(x)=-5x^2+7x+9 = -5(x^2 - (7/5)x) + 9
That's pretty ugly, but now we just need to work inside the parentheses.

Answer 6

Yeah that looks exactly how my teacher would do it. I just could never understand what to do.

Answer 7

use the formula for vertex form of

y=a(x-h)^2+k, a=-5 , b=7 c=9, vertex x=-b/2a =7/10 yes or no?whats k or y coordinate of vertex?

Answer 8

your vertex in that formula is V(h,k)

Answer 9

Now we need that thing you have burned into your brain. Let's hold them up next to each other and see what it looks like.

\(a^{2} + 2ab + b^{2}\)

\(x^{2} - \frac{7}{5}x\)

Remember those b-parts? The \(b^{2}\) is missing. The plan is to use the 'ab' term to build it.

Answer 10

mark_o I'm not really understanding how you are solving it. Thank you for your help but I think I'm going to stick with the way that tkhunny is walking me through it since it is more like the way my teacher does it.

Answer 11

How do you build it? this is the part I get stuck at the most...

Answer 12

if vertex x=7/10 then sub this to f(x)=y=-5x^2+7x+9, is y=k=229/20=11.45 yes or no ?
then sub these h and k to the formula of vertex form

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

Answer 13

a=-5,h=7/10=0.7, k=229/20=11.45 just plug them to the formula

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

Answer 14

See how the \(x^{2}\) matches up with the \(a^{2}\)? This gives us permission to pull the 'x' out of the middle term and be left with the '2b' part,

So, \(x^{2}\) relates to \(a^{2}\),
And (-7/5)x relates to 2ab. This says 2b = -7/5.

Answer 15

okay but how do i find the a.o.s and the vertex?

Answer 16

Let's not get ahead of ourselves. We still need to find the b^2 -part.

We have 2b = -7/5. Well, then b = -7/10. This leads immediately to b^2 = 49/100.