<p>18) because f(a) is the functional value of a. the question gives us the point (a, b). The functional value of a is b. so b ≤ f(a) basically means b ≤ b, which is true because b = b. b is not less than b, but it is equal to b. so it is true</p>
<p>15) i think you meant to say question 15 on page 427, not question 17. the question says the length of PQ is equal to 6. the parabola y = x^2 is equally cut by the y-axis. that means the y-axis cuts PQ into 3 and 3. we know the 2 points of intersection of the 2 parabolas have x-values of -3 and 3 because at the y-axis the x-value is 0. plug in the x-values of -3 and 3 into the equation</p>
<p>y = x^2
y = 9</p>
<p>so the point is (-3, 9) and (3, 9)
these 2 points are the points where both parabolas intersect. that means the point is on both parabolas, and should fit into both equations.</p>
<p>plug in the points in the other equation
y = a - x^2
9 = a - 9
add 9 on both sides
18 = a</p>