Answer:
a = 3, b = - 1
Step-by-step explanation:
Given the 2 equations
3a + 2b = 7 → (1)
a - 2b = 5 → (2)
Rearrange (2) expressing 2b in terms of a
2b = a - 5 ← Substitute into (1)
3a + a - 5 = 7
4a - 5 = 7 ( add 5 to both sides )
4a = 12 ( divide both sides by 4 )
a = 3
Substitute a = 3 into (1 ) or (2 ) for corresponding value of b
Using (1 )
9 + 2b = 7 ( subtract 9 from both sides )
2b = - 2 ( divide both sides by 2 )
b = - 1
Answer: repeat the question or type it correctly
Step-by-step explanation:
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)