Question

Write a quadratic that represents the table . please Explain how you created your equation

Answer 1

a quadratic equation is of the form

`y=ax^2+bx+c`

then. if x = 0, y = 7:

`\begin{gathered} 7=a(0)^2+b(0)+c \\ c=7 \end{gathered}`

and, if x = 1, y = 16

`\begin{gathered} 0=a(1)^2+b(1)+7 \\ 0=a+b+7 \\ a+b=-7\text{ eq 1 } \end{gathered}`

and if x = 2, y = 27

`\begin{gathered} 27=a(2)^2+b(2)+7 \\ 27=4a+2b+7 \\ 27-7=4a+2b+7-7 \\ 4a+2b=20\text{ } \\ 2a+b=10\text{ eq2} \end{gathered}`

then solve for a and b with the equations 1 and 2

`\begin{gathered} \begin{bmatrix}a+b=-7 \\ 2a+b=10\end{bmatrix} \\ a+b=-7 \\ a+b-b=-7-b \\ a=-7-b \\ 2\mleft(-7-b\mright)+b=10 \\ -14-2b+b=10 \\ -14-b=10 \\ -14-b+14=10+14 \\ -b=24 \\ (-b)/(-1)=(24)/(-1) \\ b=-24 \end{gathered}`

for a

`a=-7-b=-7-(-24)=-7+24=17`

answer, the equation is:

`y=17x^2-24x+7`