Parabolas

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Math

You may be asking what is math. That is a answer you can find here,Math is the study of the measurement, properties, and relationships of quantities and sets, using numbers and symbol.


There are a lot of units/lessons in math this site will help you under stand just a few for example vertex form, factored form, and standard form.

Vertex Form

The standard equation of a parabola is. y = ax^2+ bx + c. But the equation for a parabola can also be written"vertex form": y= (x-h)^2+k. In this equation, the vertex of the parabola is the point (h, k).

Few things done while teaching vertex form are. Axis of symmetry, Optimal Value, Transformations, X-intercepts, and the Step pattern

I am going to be teaching you a bit about all of these topics today

Axis of symmetry

The axis of symmetry of a parabola is a vertical line that divides the parabola into two half's . The axis of symmetry always passes through the vertex of the parabola. The x-coordinate of the vertex is the equation of the axis of symmetry of the parabola. Here is how you find the axis of symmetry. First you have to find two points on the x-axis of the parabola and then you add them and divide it by 2.
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Optimal Value

The optimal value is basically the minimum or maximum value of the parabola. Minimum value is when the parabola is opening up. maximum value is when the parabola is opening down.
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Transformation

Transformation is basically the movement of the graph. some ways the equation can show the movement of the parabola is the horizontal translation,vertical translation,vertical stretch. vertical stretch is basically how much you times the step table by each time, horizontal translation is basically the movement of the parabola left or right, and vertical stretch is the movement of the parabola up or down.
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X-intercept

To find the x-intercept you have to set y=0.
y=a(x-h)^2+k
y=3(x+1)^2-108
0=3(x+1)^2-108
+108 +108
108=3(x+1)^2
divide 108 and 3 by 3
36=(x+1)^2
square root 36 and it will cancel out the squared because what you do to one side of the equation you have to do to the other.
6=(x+1)
-1 -1
5=x
This is how you find the x-intercept by putting y=0

Step pattern

This is basically the way a normal parabola would go. (over one up 1)(over 2 up 4).
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Factored Form

The process of breaking apart of an equation into factors (or separate terms) such that when the separate terms are multiplied together, they produce the original equation. factored form is y= a(x-r)(x-s)

These are few things done while teaching factored form. Zeros(x-intercept), Axis of symmetry,optimal value.

I will be teaching you a little bit of all these topics

X-intercept using factored form

For factored form there will be a different equation, it would y= a(x-r)(x-s) and if your question is given like this that means the x-intercepts are given to you they are the r and the s in the equation. There is just one rule to remember if the number is positive it is negative on the graph and if the number is negative it will be positive on the graph.

Axis of symmetry

For factored form you are basically going to add the r and the s once you are finished that you just have to divide the total by 2 and you will have your axis of symmetry.

Optimal Value

Optimal value is basically the minimum or maximum value of a graph. and in factored form you can find out if you will be looking for minimum or maximum by the the number in front of the barracks.

Standard form

The standard form is ax² + bx + c = y with a, b, and c being constants, or numerical coefficients, and x is an unknown variable.

X-intercepts

In standard form you will have a equation like the one above. and to find the x-intercept you must first turn y to 0. and then you must factor the equation and then like stated earlier your x-intercepts will be r and s.
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Axis of symmetry

The axis of symmetry of a parabola is a vertical line that divides the parabola into two half's . The axis of symmetry always passes through the vertex of the parabola. The x-coordinate of the vertex is the equation of the axis of symmetry of the parabola. Here is how you find the axis of symmetry. First you have to find two points on the x-axis of the parabola and then you add them and divide it by 2.

Completing the square to get vertex form

You have to change equation y=(-2x^2+8x)+7 to vertex form.

y=(-2x^2+8x)+7

To get the number you have to do (b/2)^2

y=(-2x^2+8+16-16+7)

y=(-2x^2+8+16)-16+7

y=(-2x^2+8+16)-9

y=(-2x+4)^2-9

what your left with is completing a square to get vertex form

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Different types of equations

Common factoring, simple trinomial, complex trinomial, difference of squares, perfect, and factoring by graphing.

Video of how to find x and y intercepts from vertex

Math 1234