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Finding the vertex form of the graph
1. Find the vertex of the parabola
2. Pick a clear coordinate other than the vertex
3. Substitute the vertex and the other coordinate in vertex form
y = a(x - h)^2 + k
Vertex: (2, 0)
(h, k)
Vertex: (2, 0)
Coordinate: (4, 4)
Coordinate: (4, 4)
(x, y)
y = a(x - 2)^2 + 0
Remember the sign changes for the h, when you put it in an equation
4 = a(4 - 2)^2 + 0
Now you have to find the "a" value so it could be a complete equation. So you have to isolate "a"
For an equation you need 3 parts: the AOS ("h"), optimal value ("k") and the step pattern "a".
1. Brackets
4 = a(2)^2 + 0
4 = a(4) + 0
4 - 0 = a(4) + 0 - 0
4 - 0 = 4a
4 = 4a
3. Bring the 0 to the other side. When it goes to the other side, the sign changes signs.
2. Exponents
4. The zero would cancel out and the equation would look like this.
5. Subtract 4 - 0
6. Divide 4 on each side, now the "a" is isolated
4 = 4a
4 4
1 = a
THE ANSWER
4 = 1(4 - 2)^2 + 0
How you find the "a" value?
y = 1(x - 2)^2 + 0
y = (x - 2)^2
4. Vertex form equations only have 3 parts: the "h", "k" and "a" value.
5. After, you take the (x, y) coordinate out it becomes like this
You don't write the 1 or the 0
y = (x - 2)^2
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