X-Intercept Functions

1. Find the axis of symmetry.
y = x2 + 5x – 7

Completing the square, we have
So the axis of symmetry is x = -5/2

2. Solve. 5(x – 2)2 = 3

, so

3. Solve by completing the square.
x2 + 2x – 8 = 0

so , therefore x = 4 or x =

4. Find the x-intercepts.
y = x2 + 5x + 2

Setting x2 + 5x + 2 = 0, we have , or
, therefore , and
so the two x-intercepts are

5. Is the following trinomial a perfect square? Why?
x2 + 18x + 81

Yes, because it is

6. The demand and supply equations for a certain item are given by
D = -5p + 40
S = -p2 + 30p – 8
Find the equilibrium price.

-p2 + 35p – 48=0, so p2 – 35p+48=0, , we have two equilibrium prices,

7. Solve by using the quadratic formula. 5×2 + 5x = 3

8. Find the constant term that should be added to make the following expression a perfect-square trinomial.
x2 + 7x

x2 + 7x + 49/4

9. Identify the axis of symmetry, create a suitable table of values, then sketch the graph (including the axis of symmetry).

y = x2 – 4x

y = x2 – 4x = , axis of symmetry: x = 2

x y
2 -4
0 0
4 0

10. Identify the axis of symmetry, create a suitable table of values, then sketch the graph (including the axis of symmetry).

y = -x2 + 3x – 3

y = -x2 + 3x – 3 =
axis of symmetry: x=3/2
y-intercept: -3, No x-intercept because

x y
3/2 -3/4
0 -3