SOLUTION: Evaluate the discriminant b^2 - 4ac. Then use the answer to state how many real-number solutions exist for the equation. y = x^2 + 8x + 16

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Question 172247This question is from textbook Introductory Algebra
: Evaluate the discriminant b^2 - 4ac. Then use the answer to state how many real-number solutions exist for the equation.
y = x^2 + 8x + 16 This question is from textbook Introductory Algebra

Found 2 solutions by nerdybill, KnightOwlTutor:
Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
For:
y = x^2 + 8x + 16
a = 1
b = 8
c = 16
.
discriminant b^2 - 4ac
= 8^2 - 4(1)(16)
= 64 - 64
= 0
.
Since discriminant = 0, there is only "one real solution".
Answer by KnightOwlTutor(293)   (Show Source): You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=0 is zero! That means that there is only one solution: .
Expression can be factored:

Again, the answer is: -4, -4. Here's your graph:
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