I also need the the equation in standard vertex form and the axis of symmetry and the direction of opening

Hello Cari. My name is Vanessa and I will be able to help you with your question.

Now, before I begin I have a question about the problem you submitted. In order to determine the vertex form, axis of symmetry, and direction of opening you must have a quadratic function. In other words, a function that has the highest degree (exponent) of 2. The problem you submitted is a cubic function, or has a degree of 3. Cubic functions are not parabolas ("U-shaped"), like quadratic functions, so they do not have an axis of symmetry or direction of opening.

Did you mean to write **y = 5(x+2) ^{2 }**instead of y = 5(x+2)

^{3 }?

If you did mean y = 5(x+2)^{2} you can find:

1) **Vertex Form. **Remember that vertex form is written as *
y = a(x - h)*^{2} *+ k*, where the *a* value determines the direction of opening (if
*a* > 0, then it opens upwards and if *a* < 0, then it opens downward);
*h* represents the x-coordinate of the vertex; *k* represents the y-coordinate of the vertex*;
**x* and *y* represent the x- and y-coordinates of a point on the parabola, other than the vertex.

Let's find each of the values so they will be easily accessible later.

**y = a(x - h) ^{2} + k**

** **y = 5(x + 2)^{2} + 0

y = 5(x - (-2))^{2} + 0

* a*

**= 5,**

*h =*-2,*k*= 0** **(Since there is no *k* value,
*k *is zero.)

2)** Axis of Symmetry.** The axis of symmetry is a line that intersects the vertex of a parabola, through the x-axis, thus creating two symmetrical (mirrored) images. In vertex form, you can find the axis of symmetry using the form of
*x = h* because the line will have the x-coordinate of the vertex. So, the axis of symmetry is
**x = -2.**

** **

**
**3)

**Direction of Opening**. The direction of opening refers to whether the parabola opens upward (right side up "U") or opens downward (upside down "U"). Since the

*a*value is 5, and 5 is positive, then the parabola will

**open upwards.**

Feel free to respond with any questions or comments.

I hope this helps,

Vanessa

(The Math Lady)