SOLUTION: Write the quadratic function in the form y = a(x - h)2 + k. Find the veertex, axis of symmetry, domain and range
y = -2x2 - 8x - 5
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-> SOLUTION: Write the quadratic function in the form y = a(x - h)2 + k. Find the veertex, axis of symmetry, domain and range
y = -2x2 - 8x - 5
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Question 316858: Write the quadratic function in the form y = a(x - h)2 + k. Find the veertex, axis of symmetry, domain and range
y = -2x2 - 8x - 5 Answer by solver91311(24713) (Show Source):
Divide the coefficient on the term by 2 and square the result.
Add 4 inside the parentheses and outside the parentheses
Factor the perfect square in the parentheses:
Vertex:
Axis of symmetry:
Domain: (All real numbers, just like any other polynomial function)
Range: The lead coefficient is negative, therefore the parabola opens downward and the vertex represents a maximum value of the function. That maximum value is the -coordinate of the vertex, namely . The range is unconstrained less than the maximum, so Range:
You didn't ask for the intercepts, but here they are anyway:
The -intercept is at the value of the function when , so:
and the -intercept is
The -intercepts are the roots of:
Verification of that last step is left as an exercise for the student.
