The full vertex equation is and each variable represent different things on the parabola. We first started by looking at the variable a, which when gets put into an equation, changes the width of the parabola. The higher the number, the narrower the parabola and if it is negative it reflects the parabola over the x-axis. Parabolas can concave up or downwards. When it concaves up, the a must be positive and when it concaves down the a is negative.
Next, we focused on how h effects the parabola. When a number is replaced for h in an equation, it changes the height of the vertex. The variable h represents the x-coordinate of the vertex. Then, we added k to the end of the equation. K changes the placement of the vertex on the y-axis. The variable k represents is the y-coordinate of the vertex. Finally, you put all of the variables into one equation to equal y=a(x-h)^2+k. |
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Vertex to Standard: To solve from vertex to standard form you first start by expanding thee squared parentheses. Then, it helps to create an area diagram, to visualize the problem. Then you take the new equation you made, using the area diagram and put the added number outside the parenthesis. Finish the math and remove parenthesis ad now it is in standard form.
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Factored to Standard: Put the factored equation into an area diagram and ignore the A (for now). Then place your newly made form inside parenthesis after your A. Take the A and multiply it by each number. Once the math is done, it is in proper standard form.
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Standard to Vertex: Going from standard to vertex form is basically doing the opposite as what is above. I take the original problem and put parenthesis around the beginning because it helps me visualize it better. Then, create the area diagram and create your final problem. Do the math at the end of the equation and then its in vertex form.
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Standard to Factored: Start with your standard form problem and create an area diagram. This diagram will help you view what factored form looks like. Simply take the diagram and place it into the factored form equation.
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This worksheet was a very challenging one for me and many other people as well. Basically, we had to use quadratic equations to solve for 'x' and figure out how far the boat was from the shore. I was personally very confused, but at the end I understood it much better because my peers helped me throughout the problem.
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This worksheet was to help us convert from standard form to vertex form. This was one of the worksheets that finally clicked in my mind. I understood how to do this before many of my peers, so I got to go and help them out. We had to use the same formula and patterns every time to get the correct answers.
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