# Question #5d6a0

Oct 27, 2017

$x = 4 , 6$

#### Explanation:

The y-intercept $\left(0 , y\right)$ is when $x = 0$. The x-intercept $\left(x , 0\right)$ is when $y = 0$. So to find the x-intercept we will set $y = f \left(x\right)$ to $0$ and solve for $x$.
$f \left(x\right) = - 3 {\left(x - 5\right)}^{2} + 3$
$0 = - 3 {\left(x - 5\right)}^{2} + 3$
$0 = - 3 \left({x}^{2} - 10 x + 25\right) + 3$
$0 = - 3 {x}^{2} + 30 x - 75 + 3$
$0 = - 3 {x}^{2} + 30 x - 72$
$0 = - 3 \left({x}^{2} - 10 x + 24\right)$
$0 = - 3 \left(x - 6\right) \left(x - 4\right)$

$x - 6 = 0$
$x = 6$

$x - 4 = 0$
$x = 4$

so $x = 4 , 6$
You should also double-check your answers by plugging the values back into the original question. Sometimes the answers you get can be erroneous.