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Answer:
irrational
Step-by-step explanation:
See the image for a Venn diagram illustrating relationships among the various subsets of real numbers.
1. A parabola is the graph of the function
(0, 15 ) is a point of this parabola, so
So c=15, which means we decrease the number of unknowns and write again:
2. Now, since (4, -1) is another point in the parabola:
16a+4b=-16
dividing by 4:
4a+b=-4
We also know that -b/2a gives the x-coordinate of the vertex:
-b/2a=4
-b=8a
b=-8a
Substitute b=-8a in 4a+b=-4,
we get 4a-8a=-4
-4a=-4
a=1, then b=-8
So y=f(x)=x^2-8x+15
The roots of the expression, which are the x-intercepts can be found by solving the equation:
solution 1: x-4=1, x=5
solution 2: x-4=-1, x=3
The x-intercepts are (3, 0) and (5, 0)
(0, 15 ) is a point of this parabola, so
So c=15, which means we decrease the number of unknowns and write again:
2. Now, since (4, -1) is another point in the parabola:
16a+4b=-16
dividing by 4:
4a+b=-4
We also know that -b/2a gives the x-coordinate of the vertex:
-b/2a=4
-b=8a
b=-8a
Substitute b=-8a in 4a+b=-4,
we get 4a-8a=-4
-4a=-4
a=1, then b=-8
So y=f(x)=x^2-8x+15
The roots of the expression, which are the x-intercepts can be found by solving the equation:
solution 1: x-4=1, x=5
solution 2: x-4=-1, x=3
The x-intercepts are (3, 0) and (5, 0)