56 POINTS
Step 1: Analyze the graph.

Daredevil Danny takes a practice jump as shown on the graph below. Complete the steps to determine the equation for the parabolic trajectory of his practice jump.



⦁ What are the key aspects of any parabola? What do the key aspects tell you about the graph?

(5 points)




⦁ What are the key aspects of Daredevil Danny’s practice jump shown in the graph provided? Describe each value and how it is determined. (10 points)


Step 2: Solve for coefficient a.

⦁ What equation is used to find the vertex form of a parabola with the vertex (h, k)? (5 points)



⦁ Solve for the coefficient a in the vertex form for the parabola in Daredevil Danny’s practice jump using key aspects from step 1. As you solve for the coefficient, explain each step of the process in detail. (15 points)


















⦁ What is the vertex form of the parabola from Daredevil Danny’s practice jump? (5 points)

Answer:

Step 1:

What are the key aspects of any parabola? What do the key aspects tell you about the graph?

(5 points)

        0=a(4-24)^2+50

       -50=a(4-24)^2

        4-24

       -20^2=400

        -50=a(400)

       -50=400a

         -50/400=-0.125

         a = -0.125

B.) What are the key aspects of Daredevil Danny’s practice jump shown in the graph provided? Describe each value and how it is determined. (10 points)

The roots and vertex, you can find the vertex by using vertex form y=a(x-h)^2+k. You find the roots by solving the quadratic equation.

Step 2: Solve for coefficient a.

a.) What equation is used to find the vertex form of a parabola with the vertex (h, k)? (5 points)

                                               f(x) = a(x-h)^2 +k

b.) Solve for the coefficient a in the vertex form for the parabola in Daredevil Danny’s practice jump using key aspects from step 1. As you solve for the coefficient, explain each step of the process in detail. (15 points)

Not sure about this one...?

c) What is the vertex form of the parabola from Daredevil Danny’s practice jump? (5 points)

f(x)=-12/25(x-25)^2+32

The equation of Daredevil Danny's jump in vertex form is y = -0.32(x - 25)^2 + 32

The graph that completes the question is added as an attachment

These are the vertex and the intercepts of the graph.

The intercepts tell us about when the time of flight and the time of landing, while the vertex tell about the maximum height of Danny's jump.

From the graph, we have:

A quadratic function is represented as:

y = a(x - h)^2 + k

Where:

vertex = (h,k)

So, we have:

y = a(x - 25)^2 + 32

Substitute the value of the x-intercept

0 = a(15 - 25)^2 + 32

Subtract 32 from both sides

a(15 - 25)^2 = -32

Solve for a

a = -0.32

Hence, the value of the coefficient a is -0.32

So, the equation in vertex form is y = -0.32(x - 25)^2 + 32

Read more about quadratic functions at:

https://brainly.com/question/1214333

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