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Question
Write y=2x^2 - 8x + 3 in the form y = a(x-h)^2 + k. Identify the vertex, axis of symmetry, y-intercept, x-intercepts, and range
y = 2(x^2 - 4x +3/2)
x^2 - 4x + 3/2 = x^2 - 4x + 4 - 5/2 = (x-2)^2 - 5/2
so y = 2((x-2)^2 - 5/2) and then
y = 2(x-2)^2 - 5
From this we see that the vertex is (2,-5).
The axis of symmetry is x=2.
The y intercept is 3 (put 0 in for x and find y)
The x intercepts are 2 + (5/2)^1/2 and 2 - (5/2)^1/2 (put 0 in for y and solve for x)
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Socrates
Expertise
I can answer questions from the standard four semester Calculus sequence. I am not prepared for questions on Tensor Calculus. Everything else is welcome. Derivatives, partial derivatives, ordinary differential equations, single and multiple integrals, change of variable, vector integration (Green`s Theorem, Stokes, and Gauss) and applications.
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Ph.D. in Mathematics and many years teaching Calculus at state universities.
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B.S. , M.S. , Ph.D.
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