Question

graph the parabola given by the equation below. $(x + 1)^2=4(y - 3)$ provide your answer below:

Explanation:

Step1: Identify the vertex form

The standard - form of a parabola is $(x - h)^2=4p(y - k)$, where $(h,k)$ is the vertex. For the equation $(x + 1)^2=4(y - 3)$, we have $h=-1$ and $k = 3$, so the vertex is $(-1,3)$.

Step2: Identify the value of $p$

Comparing $(x + 1)^2=4(y - 3)$ with $(x - h)^2=4p(y - k)$, we get $4p = 4$, so $p = 1$. Since $p>0$, the parabola opens upwards.

Step3: Find additional points

Let's find some points on the parabola.
When $x=-3$:

$$
LATEXBLOCK0
$$

When $x = 1$:

$$
LATEXBLOCK1
$$

We can plot the vertex $(-1,3)$ and the points $(-3,4)$ and $(1,4)$ and then draw a smooth curve to graph the parabola.

Answer:

The graph of the parabola $(x + 1)^2=4(y - 3)$ has a vertex at $(-1,3)$, opens upwards, and can be drawn by plotting the vertex and additional points such as $(-3,4)$ and $(1,4)$ and connecting them with a smooth curve.