# 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

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