Question

Write a quadratic equation to match the relationship given in the table

Answer 1

In order to find the quadratic equation, let's use the standard form of a quadratic equation:

`y=ax^2+bx+c`

Using the point (0, 2) from the table, we have:

`\begin{gathered} 2=a\cdot0^2+b\cdot0+c \\ c=2 \end{gathered}`

Now, using the points (-1, -2) and (1, 22):

`\begin{gathered} -2=a(-1)^2+b(-1)+2 \\ a-b=-4 \\ 22=a(1)^2+b(1)+2 \\ a+b=20 \end{gathered}`

Adding both equations, we can solve for a:

`\begin{gathered} a-b+(a+b)=-4+(20) \\ 2a=16 \\ a=8 \\ a+b=20 \\ 8+b=20 \\ b=12 \end{gathered}`

Therefore the equation is y = 8x² + 12x + 2