SOLUTION: Yet more issues, will this homework never end? 1. Find the x-intercepts y = x² + 4x – 1 2. Evaluate the discriminant b² - 4ac. Then use the answer to state how many r

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Question 185908: Yet more issues, will this homework never end?
1. Find the x-intercepts
y = x² + 4x – 1

2. Evaluate the discriminant b² - 4ac. Then use the answer to state how many real number solutions exist for the equation.
y = x² + 8x + 16
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Yet more issues, will this homework never end?
It will end once you're out of school and in prison.
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1. Find the x-intercepts
The x-intercepts are where the graph crosses the x-axis and y = 0. These are the zeroes of the equation, the values of x that make the eqn = 0. In other words, the answers.
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y = x² + 4x – 1
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
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=20 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 0.23606797749979, -4.23606797749979. Here's your graph:

----------------------
2. Evaluate the discriminant b² - 4ac. Then use the answer to state how many real number solutions exist for the equation.
y = x² + 8x + 16
The onsite solver does a good job of that.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
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=128 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 1.65685424949238, -9.65685424949238. Here's your graph:
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