Question

Y = -2(x-5)^2 + 9 find the x axis intercepts

Answer 1

Given the following quadratic function:

`y=-2\left(x-5\right)^2+9`

We will find the x-intercepts which are the values of (x) to make y = 0

So, we will substitute y = 0, then solve the equation to find (x):

`\begin{gathered} -2\left(x-5\right)^2+9=0 \\ 2(x-5)^2=9 \\ (x-5)^2=(9)/(2) \\ \end{gathered}`

Taking the square root of both sides:

`\begin{gathered} x-5=\pm\sqrt{(9)/(2)} \\ x-5=\pm(3√(2))/(2) \\ \\ x=5\pm(3√(2))/(2) \end{gathered}`

So, the answer will be:

`x-intercepts=\lbrace5-(3√(2))/(2),5+(3√(2))/(2)\rbrace`