Question

write a quadratic function in standard form whose graph passes through the given points1. (-1,5), (0,3), (3,9)2. (1,2), (3,4), (6,-8)

Answer 1

We have the following:

We must find the equation in each case, first calculating the slope and then the intercept with y, and finally we go to the standard form

The slope is:

`m=(y_2-y_1)/(x_2-x_1)`

1. (-1,5), (0,3), (3,9)

`m=(9-5)/(3-(-1))=(4)/(3+1)=(4)/(4)=1`

now, for intercept with y:

x = 0, y = 3

m = 1

`\begin{gathered} y=mx+b \\ 3=1\cdot0+b \\ b=3 \end{gathered}`

The standard form:

`\begin{gathered} y=x+3 \\ y-x=3 \end{gathered}`

2. (1,2), (3,4), (6,-8)​

`m=(-8-2)/(6-1)=(-10)/(5)=-2`

now, for intercept with y:

x = 3, y =4

m = -2

`\begin{gathered} y=mx+b \\ 4=-2\cdot3+b \\ b=4+6 \\ b=10 \end{gathered}`

The standard form:

`\begin{gathered} y=-2x+10 \\ y+2x=10 \end{gathered}`