1. ## Finding a quadratic function from given information

Using this information, can you find the quadratic equation.

Y intercept- (o,-8)

X intercepts- (1,0) and (4,0)

Please try, because i jut do not understand ANY of it

2. Hello Tessarina
Originally Posted by Tessarina
Using this information, can you find the quadratic equation.

Y intercept- (o,-8)

X intercepts- (1,0) and (4,0)

Please try, because i jut do not understand ANY of it
Suppose the equation is of the form $\displaystyle y = ax^2+bx+c$. Then plug in each of the pairs of values of $\displaystyle x$ and $\displaystyle y$ in turn:

$\displaystyle (0,-8):-8 = a0^2+b0+c$
$\displaystyle \Rightarrow c = -8$
$\displaystyle (1,0):0 = a+b+c$
$\displaystyle \Rightarrow a+b=8$ (1)
$\displaystyle (4,0): 0 = 16a+4b+c$
$\displaystyle \Rightarrow 16a+4b=8$
$\displaystyle \Rightarrow 4a+b=2$ (2)
Now solve the simultaneous equations (1) and (2) to find $\displaystyle a$ and $\displaystyle b$, and plug the answers back into the original equation to get
$\displaystyle y=-2x^2+10x-8$
Can you fill in the working?