1) Match the Vertex Form equation to the given graph by moving the sliders to set your "a", "h" and "k" values. Write out the example given on your paper, then write the equation that fits the example.
**If you need to be more precise click on the slider and use your left and right arrows on your laptop. To get more practice, click on the "New Equation" button and try again.
**If you need to be more precise click on the slider and use your left and right arrows on your laptop. To get more practice, click on the "New Equation" button and try again.
In problems 2-6, given the vertex and point \(P\) on the parabola, write the equation of the parabola in Vertex Form.
2) Vertex: \((-4,-3)\) P\((-2,1)\)
3) Vertex: \((5,2)\) P\((4,5)\)
4) Vertex: \((2,3)\) P\((7,8)\)
5) Vertex: \((8,5)\) P\((10,-7)\)
6) Vertex: \((-2,7)\) P\((0,1)\)
7) Match the Intercept Form equation to the given graph by moving the sliders to set your “a”, “p”, and “q” values.Write out the example given on your paper, then write the equation that fits the example
**If you need to be more precise click on the slider and use your left and right arrows on your laptop. To get more practice, click on the "New Graph" button and try again.
In problems 8-12, given the two x-intercepts and a point on the parabola, write the equation of the parabola in Intercept Form.
8) \((3,0)\ \ (-1,0)\ \ (2,-6)\)
9) \((-5,0)\ \ (-2,0)\ \ (-1,-12)\)
10) \((-6,0)\ \ (3,0)\ \ (4,8)\)
11) \((-4,0)\ \ (10,0)\ \ (0,20)\)
12) \((-9,0)\ \ (0,0)\ \ (-3,-24)\)
13) A quarterback threw a \(54\) yard touchdown pass (horizontal distance). The ball reached a maximum height of \(21\) yards. Assuming that the ball was thrown and caught at the same height, write an equation that models the path of the ball as a function of the vertical height (y), in terms of the horizontal distance \(x\).
14) Your company just released a spreadsheet that shows the profit earned, in thousands \(y\), based on the selling price \(x\) of an item. Before you can further analyze the data, you will need to find the equation that models the situation. For the table below, find the best-fitting quadratic model. Then use it to find the profit if \(250\) items were sold.
Review
15) Given the function \(f(x)=2x^2-8x-10\), identify the vertex, domain, range, and x-intercepts.
16) Given the equation: \(0=5x^2-7x+2\)
a) Find discriminant and use it to identify the number and type of solutions.
b) Solve the equation using the method of your choice.
17) Solve the following equation: \(0=x^2+8x+19\).
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