# Where is the vertex in the parabola y = x^2 +2x - 5? i dont understand this i need x and y intercepts and please show work?

May 7, 2018

Vertex (-1, -6)

#### Explanation:

y = x^2 + 2x - 5
The x-coordinate of vertex is given by the formula:
x = - b/(2a) = - 2/2 = - 1
The y- coordinate of Vertex is given by y(-1), when x = -1 -->
y(-1) = (-1)^2 + 2(-1) - 5 = - 6
Vertex (-1, -6)
graph{x^2 + 2x - 5 [-20, 20, -10, 10]}

May 7, 2018

Vertex $\left(- 1 , - 6\right)$
Y-intercept $\left(0 , - 5\right)$
x-intercept $\left(1.449 , 0\right)$
x-intercept $\left(- 3.449 , 0\right)$

#### Explanation:

Given -

$y = {x}^{2} + 2 x - 5$

Vertex is the point where the curve turns.
To find this point - first you have to calculate
for what value of $x$ the curve turns. Use the formula to find that.

$x = \frac{- b}{2 a}$

Where -
$b$ is the coefficient of $x$
$a$ is the coefficient of ${x}^{2}$

$x = \frac{- 2}{2 \times 1} = \frac{- 2}{2} = - 1$

When $x$ takes the value $- 1$ the curve turns. At that point $x$ co ordinate is $- 1$, then what is $y$ coordinate. Plug in the $x = - 1$ in the given equation.

$y = {\left(- 1\right)}^{2} + 2 \left(- 1\right) - 5 = 1 - 2 - 5 = - 6$

At point $\left(- 1 , - 6\right)$ the curve turns. This point is vertex.

Vertex $\left(- 1 , - 6\right)$
Look at the graph.

What is $y$ intercept?
It is the point at which the curve cuts the Y-axis. Look at the graph. At $\left(0 , - 5\right)$ the curve cuts the Y-axis.
How to find it out?
Find the What is the value of $y$ when $x$ takes the value $0$

At x=0; y=0^2+2(0)-5=0+0-5=-5

At point $\left(0 , - 5\right)$ the curve cuts the Y-axis.
Y-intercept $\left(0 , - 5\right)$

What is X-intercept?

It is the point at which the curve cuts the x-axis. Look at this graph. The curve cuts the x axis at two points. Then, how to find it out. Find the value(s) of $x$ when $y = 0$

${x}^{2} + 2 x - 5 = 0$
Solve to find the value of $x$ [Squaring method is used]

${x}^{2} + 2 x = 5$
${x}^{2} + 2 x + 1 = 5 + 1 = 6$
${\left(x + 1\right)}^{2} = 6$
$x + 1 = \pm \sqrt{6} = \pm 2.449$
$x = 2.449 - 1 = 1.449$

x-intercept $\left(1.449 , 0\right)$

$x = - 2.449 - 1 = - 3.449$

x-intercept $\left(- 3.449 , 0\right)$