y=f(x)= -2x^2+12x-10: find vertex, intercepts, max, graph

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
tphillips9
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y=f(x)= -2x^2+12x-10: find vertex, intercepts, max, graph

Postby tphillips9 » Tue Dec 01, 2009 9:19 pm

y=f(x)= -2x^2+12x-10 represent a parabola. Determine (a)the vertex (b) x and y intercepts (c) the maximum value of y and (d) sketch the graph of the parabola

nona.m.nona
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Re: y=f(x)= -2x^2+12x-10: find vertex, intercepts, max, graph

Postby nona.m.nona » Wed Dec 02, 2009 1:14 am

Either complete the square to find the vertex, or else use the formula.

To find the x-intercepts, plug zero in for y. To find the y-intercepts, plug zero in for x.

The maximum will be the y-value of the vertex.

To graph, draw the vertex and the intercepts, and plot a few more points. Then draw the graph.

tphillips9
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Re: y=f(x)= -2x^2+12x-10: find vertex, intercepts, max, graph

Postby tphillips9 » Sat Dec 05, 2009 3:16 am

is the vertex 1/8 and the x and y intercept is (1/2,0) or (-10,0) and y is (0,10)

nona.m.nona
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Re: y=f(x)= -2x^2+12x-10: find vertex, intercepts, max, graph

Postby nona.m.nona » Sat Dec 05, 2009 12:42 pm

The vertex is supposed to be a point, (x, y) = (h, k). Try using the formula to get the value of h, and then plug that into f(x) to find the value of k.

To find the intercepts, plug in zeroes where appropriate. To find the x-intercepts, either factor or else use the Quadratic Formula. To find the y-intercept, simply evaluate.

If you are unsure of your answers, please reply showing your work. Thank you.


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