The equation of Daredevil Danny's jump in vertex form is y = -0.32(x - 25)^2 + 32
The values of the coefficients a, b and c
The graph of Daredevil Danny's jump is added as an attachment
A quadratic function is represented as:
y = a(x - h)^2 + k
From the graph, we have:
- Vertex, (h, k) = (25,32)
- x-intercepts = 15 and 35
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
Substitute a = -0.32 in y = a(x - 25)^2 + 32
y = -0.32(x - 25)^2 + 32
Expand the exponent
y = -0.32(x^2 -50x + 625) + 32
Expand the bracket
y = -0.32x^2 + 16x - 200 + 32
This gives
y = -0.32x^2 + 16x - 168
Hence, the values of the coefficients a, b and c are -0.32, 16 and -168
Did he jump successfully?
Yes, he jumped successfully
This is so because his maximum height (i.e. the vertex of his jump) is higher than the vertex of the hoop
Read more about quadratic functions at:
https://brainly.com/question/22679014
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