I also need the the equation in standard vertex form and the axis of symmetry and the direction of opening
What is the vertex of y=5(x+2)^3
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,
(The Math Lady)