SOLUTION: I have a graphing problem and it is driving me crazy!!!! It is hard for me to explain it. But I will try. The problem is using a graph of y=-x^2+4x+5 but without solving the equati

Algebra ->  Functions -> SOLUTION: I have a graphing problem and it is driving me crazy!!!! It is hard for me to explain it. But I will try. The problem is using a graph of y=-x^2+4x+5 but without solving the equati      Log On


   

Question 163024: I have a graphing problem and it is driving me crazy!!!! It is hard for me to explain it. But I will try. The problem is using a graph of y=-x^2+4x+5 but without solving the equation, or factoring, determing the solution to the equation -x^2+4x+5=0 but we have to use a graph!
The second problem is, but i'm not sure what is meant by calculate the value of discriminant of x^2+x+3=0?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Graph:
y+=+-x%5E2%2B4x%2B5
graph%28400%2C400%2C-5%2C10%2C-5%2C10%2C-x%5E2%2B4x%2B5%29
From the graph, you can see that the parabola crosses the x-axis at x = -1 and x = 5.
These are the "zeros", also known as the solutions, of the equation.
The "discriminant" of a quadratic equation is the quantity under the radical when you use the quadratic formula x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a to solve.
So the discriminanat is (b%5E2-4ac)
In this case, you have:
x%5E2%2Bx%2B3+=+0
Now as you can see, the "discriminant" is (b%5E2-4ac+=+1%5E2-4%281%29%283%29 = 1-12+=+-11
So the disciminant is negative which means that the solution to the quadratic equation: x%5E2%2Bx%2B3+=+0 will have a solution consisting of two complex conjugate roots. In other words, the graph of this equation does not intersect the x-axis. See the graph below:
graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Cx%5E2%2Bx%2B3%29