d) What are the values for coefficients a, b, and c in the quadratic equation for Daredevil Danny’s practice jump? (5 points)
2 answers:
Answer:
a = -0.32
b = 16
c = - 168
Step-by-step explanation:
In the figure attached, the quadratic function is shown. We can model it as follows:
y = a*(x - x1)*(x - x2)
where (x1, 0) and (x2, 0) are its roots
From the picture, roots are (15, 0) and (35, 0), replacing them into the equation:
y = a*(x - 15)*(x - 35)
and the vertex is at (25,32), replacing into the equation:
32 = a*(25 - 15)*(25 - 35)
32 = a*(-100)
a = 32/(-100)
a = -0.32
Applying distributive property:
y = -0.32*(x - 15)*(x - 35)
y = -0.32*(x² - 35x - 15x + 525)
y = -0.32x² + 16x - 168
which corresponds to the general form:
y = ax² + bx + c
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The problem has asked that we write a point-slope equation of the line in the image above. Point-Slope Form uses the following formula:
y –
In this case, M represents the slope while
We are given that the slope of the line is -
y – 2 = -
We have now successfully created an equation based on the information given in the problem above. Looking at the four possible options, we can now come to the conclusion that the answer is C.
I hope this helps!