Equation help 2 questions

How many real number solutions does the equation have

y=-4x^2+7x-8
none
one
two
infinite

How many real number solutions does the equation have
y=3x^2+18x+27
none
one
two
infinite

Thank you!

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  1. is number 1 none?

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  2. Mrs sue can you help me with question 2?

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  3. You state the equation as a function, so to speak of real number solutions makes no sense.
    There are an infinite number of solutions, any ordered pair satisfying the equation would be one.
    You probably want the solution to
    -4x^2 + 7x - 8 = 0

    in both cases, it depends on the value of the discriminant b^2 - 4ac

    for the first:
    b^2 - 4ac
    = 49-4(-4)(-8) = negative
    So -4x^2 + 7x - 8 = 0 has no real solution
    here is your graph, notice that the curve does not reach the x-axis
    http://www.wolframalpha.com/input/?i=plot+y%3D-4x%5E2%2B7x-8+

    for 3x^2 + 18x + 27 = 0
    b^2- 4ac
    = 18^2 - 4(3)(27) = 0

    so there is ONE real solution

    verification:
    http://www.wolframalpha.com/input/?i=plot+y%3D3x%5E2%2B18x%2B27

    graph touches the x-axis once, so one solution.

    You should make yourself familiar to the properties of solutions of a quadratic based on the sign of b^2 - 4ac
    This should be found in your text or your notes.

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