Please help me change this standard form of a parabola to vertex form.
y = 0.2955x^2 + 0.1811x + 22.382
If possible, please use the -b/2a version instead of completing the square, because that is what I was taught.
Thank you for any help!
Please help me change this standard form of a parabola to vertex form.
y = 0.2955x^2 + 0.1811x + 22.382
If possible, please use the -b/2a version instead of completing the square, because that is what I was taught.
Thank you for any help!
completing the square for $\displaystyle y = ax^2 + bx + c$
$\displaystyle y = a \bigg( x^2 + \frac bax + \frac ca \bigg)$
$\displaystyle \Rightarrow y = a \bigg[ x^2 + \frac bax + \left( \frac b{2a}\right)^2 - \left( \frac b{2a} \right)^2 + \frac ca \bigg]$
$\displaystyle \Rightarrow y = a \bigg[ \left( x + \frac b{2a}\right)^2 + \frac {4ac - b^2}{4a^2} \bigg]$
$\displaystyle \Rightarrow y = a \bigg(x + \frac b{2a} \bigg)^2 + \frac {4ac - b^2}{4a}$
$\displaystyle y = a\left(x+\frac{b}{2a}\right)^2+\frac{4ac-b^2}{4a}$
The vertex is $\displaystyle \left(-\frac{b}{2a}, \;\frac{4ac-b^2}{4a}\right)$
here, a = 0.2955, b = 0.1811, c = 22.382
$\displaystyle y = 0.2955\left(x+\frac{0.1811}{2(0.2955)}\right)^2+\f rac{4(0.2955)(22.382)-(0.1811)^2}{4(0.2955)}$
$\displaystyle y = 0.2955\left(x+0.3064\right)^2+22.3542$