# What are the intercepts of y=2(x-3)(x+5)?

Feb 7, 2018

See below...

#### Explanation:

We know that the x intercepts of any quadratic is where the roots are $=$ to $0$

$\therefore$ using $2 \left(x - 3\right) \left(x + 5\right) = 0$

$\therefore$ $x - 3 = 0$
$\implies$ $x = 3$

$\therefore x + 5 = 0$
$\implies x = - 5$

As the roots occur at $y = 0$, we get the coordinates of intersection on the x axis are $\left(3 , 0\right) , \left(- 5 , 0\right)$

Now we need to work out the y intercept (the point where it crosses the y axis). This will always occur at $x = 0$ always giving coordinates in the form $\left(0 , y\right)$

$\therefore$ subbing $x = 0$ in the equation, we get.

$2 \left(0 - 3\right) \left(0 + 5\right)$
$2 \left(- 3\right) \left(5\right) = - 30$

$\therefore$ the y intercept is at $\left(0 , - 30\right)$

Feb 7, 2018

#### Answer:

$y = - 30 \text{ and } x = - 5 , 3$

#### Explanation:

$\text{to find the intercepts, that is where the graph crosses}$
$\text{the x and y axes}$

• " let x = 0, in the equation for y-intercept"

• " let y = 0, in the equation for x-intercepts"

$x = 0 \to y = 2 \left(- 3\right) \left(5\right) = - 30 \leftarrow \textcolor{red}{\text{y-intercept}}$

$y = 0 \to 2 \left(x - 3\right) \left(x + 5\right) = 0$

$\text{equate each factor to zero and solve for x}$

$x - 3 = 0 \Rightarrow x = 3 \leftarrow \textcolor{red}{\text{x-intercept}}$

$x + 5 = 0 \Rightarrow x = - 5 \leftarrow \textcolor{red}{\text{x-intercept}}$
graph{2(x-3)(x+5) [-10, 10, -5, 5]}