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 $y = ax^2+bx+c$. Then plug in each of the pairs of values of $x$ and $y$ in turn:

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