convert y-5=-2(X+1)^2 to quadratic intercept form

Question

jhannybean · Answer

quadratic formula follows $\large y= ax^2+bx+c$ and you have $y-5=-2(x+1)^2$

first we need o expand (x+1)^(2) = (x+1)(x+1) = $x^2+2x+1$ then multiply in the 2. $$2(x^2+2x+1)=(2x^2+4x+2)$$ in order to fit the form now, we have to add 5 to both sides, so we get $$y=(2x^2+4x+2)+5$$ we can simplify it further $$y=2x^2+4x+7$$All together, quadratic intercept form: $\large y=ax^2+bx+c$ => $\large y=2x^2+4x+7$

anonymous · Answer

Sorry but thats standard form. I'm asking for the intercept form which is y=a(x-r)(x-r)

anonymous · Answer

y - 5 = -2 X2

jhannybean · Answer

$\large y=2x^2+4x+7$= standard form$$\large \frac{y}{2}=x^2+2x+7$$complete the square$$\large \frac{y}{2}=x^2+2x+1=-\frac{7}{2}+1$$$$\large \frac{y}{2}=(x+1)^2+\frac{5}{2}$$multiply by 2 the whole thing. $$\large y=[(x+1)^2+\frac{5}{2}]*2$$$$\large y=2(x+1)^2+5$$ rearrange. $\large y-5=2(x+1)^2$ intercept form.