Question

Write the quadratic function with the indicated characteristics. The graph passes through the origin and the points (-3, 0) and (-1, 3).

Answer 1

substituteGiven:-

$(0,0),(-3,0)(-1,3)$

To find the quadratic equation.

So now we use the formula,

$y=ax^2+bx+c$

So now we subtitute the points and find the value of a,b,c. So we get,

$\begin{gathered} 0=a(0)+b(0)+c \\ c=0 \end{gathered}$

Also,

$\begin{gathered} 0=a(-3)^2+b(-3)+c \\ 0=9a-3b \end{gathered}$

Also,

$\begin{gathered} 3=a(-1)^2+b(-1)+0 \\ 3=a-b \end{gathered}$

So now we simplify both equation. so we get,

$\begin{gathered} 9a-3b=0 \\ 3a-3b=9 \end{gathered}$

Now we add both the equations. we get,

$\begin{gathered} 6a=-9 \\ a=-\frac{3}{2} \end{gathered}$

Now we find the value of b, so we get,

$\begin{gathered} a-b=3 \\ -\frac{3}{2}-b=3 \\ -b=3+\frac{3}{2} \\ -b=\frac{9}{2} \\ b=-\frac{9}{2} \end{gathered}$

So the required values are,

$y=-\frac{3}{2}x^2-\frac{9}{2}x+0$