Question

In the following exercises, graph each equation by using its properties:

$y=x^2+4x-3$

Short answer

The graph of the parabola can be given as

Step-by-step solution

Given information

We are given an equation of the parabola as$y=x^2+4x-3$

Check whether the parabola is upward or downward

As the coefficient of$x^2$is positive the parabola opens upward

Find the axis of symmetry

The axis of symmetry can be given as $x=-\frac{b}{2a}$

On substituting the values we get

role="math" localid="1645426794793" $$\begin{gathered} x=-\frac{4}{2} \\ x=-2 \end{gathered}$$

Step 4:  Find the vertex of the parabola

We know the axis of symmetry passes through the point $x=-2$

Put this in the original equation we get

$$\begin{gathered} y={(-2)}^2+4(-2)-3 \\ y=4-8-3 \\ y=-7 \end{gathered}$$

The vertex is$(-2,-7)$

To find the y-intercept put x=0

We get,

$$\begin{gathered} y=0^2+4\left(0\right)-3 \\ y=-3 \end{gathered}$$

The coordinate on parabola is $(0,-3)$

The point$(0,-3)$is two units right to the axis of symmetry Hence the point 2 units left of the axis of symmetry is$(-4,-3)$

Step 6; We write the x-intercept

To find the x-intercept we put $y=0$

$x^2+4x-3=0$

on using quadratic formula we get

$x=-4.64$and $x=0.646$

Hence the coordinates are$(-4.64,0),(0,646,0)$

plot the graph

The graph can be given as

Conclusion

The graph of the parabola can be given as