SOLUTION: {{{y=x^2/16+(21/16)x+11/8}}} (i) Is the parabola u-shaped or n-shaped? How can you tell this from the equation? (ii) Use algebra to find the x-intercepts. (iii) Explain w

Algebra ->  Graphs -> SOLUTION: {{{y=x^2/16+(21/16)x+11/8}}} (i) Is the parabola u-shaped or n-shaped? How can you tell this from the equation? (ii) Use algebra to find the x-intercepts. (iii) Explain w      Log On


   

Question 955395: y=x%5E2%2F16%2B%2821%2F16%29x%2B11%2F8
(i) Is the parabola u-shaped or n-shaped? How can you tell this from the equation?
(ii) Use algebra to find the x-intercepts.
(iii) Explain why the y-intercept is 11/8
(iv) Find the equation of the axis of symmetry, explaining your method. Use this information to find the coordinates of the vertex, rounding your answers where necessary to one decimal place.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
(i) Whether the parabola opens upwards (u) or downwards (n) is governed by the sign of the quadratic term's coefficient.
In this case, 1%2F16%3E0 so it opens upwards (u).
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(ii) To find the x-intercepts, set y=0 and solve for x
x%5E2%2F16%2B%2821%2F16%29x%2B11%2F8=0
x%5E2%2B21x%2B22=0
Complete the square.
x%5E2%2B21x%2B%2821%2F2%29%5E2%2B22=%2821%2F2%29%5E2
%28x%2B21%2F2%29%5E2=%28441%2F4%29-88%2F4
%28x%2B21%2F2%29%5E2=353%2F4
x%2B21%2F2=0+%2B-+sqrt%28353%29%2F2
x=-21%2F2+%2B-+sqrt%28353%29%2F2
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(iii) To find the y-intercept, set x=0 and solve for y
y=x%5E2%2F16%2B%2821%2F16%29x%2B11%2F8
y=0%2B0%2B11%2F8
y=11%2F8
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(iv) Similar to (ii) complete the square,
y=x%5E2%2F16%2B%2821%2F16%29x%2B11%2F8
y=%281%2F16%29%28x%5E2%2B21x%29%2B11%2F8
y=%281%2F16%29%28x%5E2%2B21x%2B%2821%2F2%29%5E2%29%2B11%2F8-%281%2F16%29%2821%2F2%29%5E2
y=%281%2F16%29%28x%2B21%2F2%29%5E2%2B88%2F64-441%2F64
y=%281%2F16%29%28x%2B21%2F2%29%5E2-353%2F64
So then the vertex occurs at (-21%2F2,-353%2F64).
The axis of symmetry is x=-21%2F2.
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