Around 1,100 scientists live in Antarctica during the winter. In the summer that number increases to around 5,000 scientists. As
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The equation of Daredevil Danny's jump in vertex form is y = -0.32(x - 25)^2 + 32
<h3>The values of the coefficients a, b and c</h3>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
<h3>Did he jump successfully?</h3>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
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