Question

Find the vertex of the quadratic function below. Write your answer in fractional form if necessary. Do not use decimals.

Answer 1

Given quadratic expression is

`f(x)=-3x^2-4x+7`

Comparing with the general quadratic function

`f(x)=ax^2+bx+c`

We have,

`a=-3,b=-4,c=7`

So, the x coordinate of the vertex is

`\begin{gathered} -(b)/(2a)=-(-4)/(-6) \\ =-(2)/(3) \end{gathered}`

Now, putting the x coordinate in the equation of the given function,we have,

`\begin{gathered} f(-(2)/(3))=-3((4)/(9))-4(-(2)/(3))+7 \\ =-(12)/(9)+(8)/(3)+7 \\ =(75)/(9) \end{gathered}`

So, the vertex of th egiven quadratic function is at

`(-(2)/(3),(75)/(9))`