Math Help - Graphing a Parabola in Standard Form

1. Graphing a Parabola in Standard Form

Sketch the graph of f(x)= 2x^2 8x + 7 and identify the vertex and the axis of the parabola.

i have no idea how to do it.

can you please give me step by step on how to do it.

like what is the first step and so on.

thank you.

2. Re: Graphing a Parabola in Standard Form

Originally Posted by Candy101
Sketch the graph of f(x)= 2x^2 8x + 7 and identify the vertex and the axis of the parabola.

i have no idea how to do it.

can you please give me step by step on how to do it.

like what is the first step and so on.

thank you.
Start by taking out 2 as a factor, then complete the square on the remaining stuff.

3. Re: Graphing a Parabola in Standard Form

ok i got this far and now im stuck, and i don't know is this step is correct

f(x)= 2(x^2 +4x+4)7-4

i do not what to do after this.

4. Re: Graphing a Parabola in Standard Form

Originally Posted by Candy101
ok i got this far and now im stuck, and i don't know is this step is correct

f(x)= 2(x^2 +4x+4)7-4

i do not what to do after this.
No, when you take out 2 as a factor, you divide every term by 2.

It should be $\displaystyle 2x^2 + 8x + 7 = 2\left(x^2 + 4x + \frac{7}{2}\right)$

Now try to complete the square on the stuff in the brackets.

5. Re: Graphing a Parabola in Standard Form

so will it be

$\displaystyle 2\left(x^2 + 4x + \frac{7}{4}+4\right)$ ???

if so then what do i do after that

i watch some videos on it, and this is what i came up with

$\displaystyle 2\left(x^2 + 4x +4 \)2(-4\right)+7$

$\displaystyle 2\left(x^2 + 4x +4 \)-8\right+7$ = $\displaystyle 2\left(x^2 + 4x +4 \)-1\right$

then i write it in standard form $\displaystyle f(x)= a\left(x- h\)^2+k\right$

isnt that correct?

6. Re: Graphing a Parabola in Standard Form

Originally Posted by Candy101
so will it be

$\displaystyle 2\left(x^2 + 4x + \frac{7}{4}+4\right)$ ???

if so then what do i do after that

i watch some videos on it, and this is what i came up with

$\displaystyle 2\left(x^2 + 4x +4 \)2(-4\right)+7$

$\displaystyle 2\left(x^2 + 4x +4 \)-8\right+7$ = $\displaystyle 2\left(x^2 + 4x +4 \)-1\right$

then i write it in standard form $\displaystyle f(x)= a\left(x- h\)^2+k\right$

isnt that correct?
No, you can't just add a term to something and expect it to be equal to what you originally started with. Whatever extra term you add, you have to subtract straight away.