Question

how do i put y=-4x^2+16x-10 into a(x-h)^2+k form?

Answer 1

Completing the square would get your there. Familiar with that technique?

Answer 2

first take the common factor -4 out of the whole equation;
then divided by what's next to x by 2, and that should be your h value, since if you square (x-h), you'll get +h^2 as the last term of the expansion, you gotta minus h^2 away from the -10/-4 result as well and that will be your k value.

Answer 3

step 1) -4(x^2-4x)-10 step 2) -4(x^2-4x+4)-10 step 3) -4(x-2)^2+4 ???? @perl

Answer 4

your step 1 is correct, step 2 need to +4 - 4 so as to remain consistent with step 1's value.

Answer 5

@mathmale yes. the part when i make perfect square and i have to make sure i add the same number outside the parenthesis as i do inside is confusing me though.

Answer 6

x^2 - 4 x + 4 is essentially (x-2)^2
so if you were to have x^2 - 4x alone, you would +4 and -4 at the end to make it (x-2)^2 - 4, since when you artificially add +4 into your x^2-4x part to make it a complete square, you also need to -4 away to keep the equation the same. that's the equivalent of adding 0 to your entire equation.

Answer 7

this is what they want. but the part where they add 45 was throwing me off

Answer 8

Are you OK with that part now, or do you still need further discussion?

Answer 9

$$\large{y=-4x^2+16x-10
\\~\\ y = -4\left( x^2 - \frac{16}{4}x \right) - 10
\\~\\ y = -4\left( x^2 - 4x \right) - 10
\\~\\ y = -4\left( x^2 - 4x + 4 - 4 \right) - 10
\\~\\ y = -4\left( x^2 - 4x + 4 \right) - 4\cdot 4 - 10
\\~\\ y = -4\left( x^2 - 4x + 4 \right) - 16 - 10

}
$$

Answer 10

yea im ok. thanks for the help @mathmale and everyone else too

Answer 11

:)

Answer 12

the -5 out front multiplies with the +9 inside to get -45

to balance things out, we need +45 since 45+(-45) = 0

Answer 13

@jim_thompson5910 that makes more sense

Answer 14

$$ \large{y=-5x^2+30x-36
\\~\\ y = -5\left( x^2 - 6x \right) - 36
\\~\\ y = -5\left( x^2 - 6x + \color{red}{0}\right) - 36
\\~\\ y = -5\left( x^2 - 6x + \color{red}{9 - 9}\right) - 36
\\~\\ y = -5\left( x^2 - 6x + 9\right) - 5 \cdot (-9) - 36
\\~\\ y = -5\left( x^2 - 6x + 9\right) + 45 - 36
\\~\\ y = -5\left( x^2 - 6x + 9\right) + 9
\\~\\ y = -5\left( x-3\right)^2 + 9
}
$$

Answer 15

this is a 'proof without words'