Math problems mostly about parabola and requires excel work

Parabolas: Alalawi_Ahmed_MA111_LehrSpring2021_parabola.txt Work problems out on separate paper, scan and upload to canvas Parabolas Discussion *** Please watch for + a negative value in problems i.e. 3 + -2 in the questions... Q1. Given the function f(x) = 7x^2 + -10x + -3 a. Determine values of A, B, C b. Does the parabola open upward or downward? c. Determine the vertex of the parabola, compute the (x,y) point. d. Determine the zeros, if any, of the parabola? Note: zeros are often referred to as roots or solutions e. Does the parabola have a maximum value or a minimum value? f. Plot the parabola. Include: zeros, the vertex, axis of symmetry Q2. Use excel to plot problem number 1 and verify your solution. Submit a screen shot and the excel document. Note: make sure you plot domain covers the line of symmetry. Note when we plot in excel, and used x increments of 1, you might not get the exact vertex as a point. Q3. The height of a projectile measured in feet, s, is governed by the equation: s(t) = -16t^2 + 446t + 87 a. Find the time it takes to reach the maximum height b. The maximum height c. Find the time it takes for the projectile to hit the ground Q4. Use excel to plot and verify your answers in problem 3 (again your resolution may effect your answer, but should be close). Q5. In quadratic functions, there are 3 possible cases for the discriminant (>0, =0, and <0), sketch there associated graphs and describe the number of zero's. Q6. Now that you have solved these problems, reflect on what you have done. In the parabolas, we see the function value change directions at the vertex, that is as x increases from negative infinity toward positive infinity what does the function do? Where is the function increasing? Where does the function reach a maximum or minimum value? Where is the function decreasing? What is the valid domain of values for each function (i.e. valid x values). What is the valid range for each function (i.e. valid y values)? Answer these in set form. i.e. ( for non inclusive, and [ for inclusive, i.e. (-inf, x_vertex] For Problem 1: domain: domain where is function is increasing ? domain where is function is decreasing ? range:

For Problem 3: domain: domain where function is increasing ? domain where function is decreasing ? range: