Question

Graph the function y = -x^2 + 10x - 25. How many solutions are there?


Two Solutions


One Solution


No Solution


Infinite solutions

Answer 1

To graph this function, we need to first find the y-intercept, which is -25. Now, to find the axis of symmetry, we can use the formula -b/2a, which would give us -10/-2 = 5. Now that we know the axis of symmetry if x = 5 and the y intercept is -25, we plug in the values -2,-1,0,1 and 2 into the function and graph. The graph would look like this;

Answer 2

I got one solution.

Answer 3

nd I'm unsure If I'm right or not

Answer 4

yes, there if only one solution according to the graph, which is x = 5. However, according to the discriminant, b^2 - 4ac, the answer is 4, which means that there are two real rational solutions. Therefore, the solution is x=5 with a multiplicity of 2.

Answer 5

Another way of finding the solutions is by factoring, which would be f(x)= -(x - 5)^2. However, since there is a binomial squared, there are two binomials with two solutions, with both of the solutions being x = 5.\[f(x) = -(x - 5)^2 = -(x - 5)(x - 5)\] \[-(5-5)(5-5) = -0+0 = 0\]

Answer 6

So really, there are two solutions, even though it appears to have only one solution on the graph

Answer 7

Thank you.