9-1 a nd 9 -2 Grap h in g Qu ad r at ic Funct ions
Quick Review Ex e r c i se s
A function of the form y = ax2 + bx + c, where a + 0, is Graph each function. Label the axis of symmetry and the
a quadratic function. Its graph is a parabola. The axis vertex.
of symmetry of a parabola divides it into two matching
halves. The vertex of a parabola is the point at which the 5. y = |x2^6. y=-x2+l
parabola intersects the axis of symmetry. 7. y = x2-4 8. y=5x2 + 8Ex a m p l e
What is the vertex of the graph of y = x 2 + 6x - 2?- y = ~\x2 + 4x + 1 10. y = -2x2 - 3x + 10
- y = |x2 + 2x-3 12. y = 3x2 + x - 5
The x-coordinate of the vertex is given by x = Open-Ended Give an example of a quadratic function that
—b —6 „
* _ 2a ~ 2(1) “matches each description.
Find the y-coordinate of the vertex. 13. Its graph opens downward.
y = (—3)2 + 6 (—3) - 2 Substitute - 3 for x. 14. The vertex of its graph is at the origin.
y=-ll Simplify. 1 5. Its graph opens upward.Thevertexis (-3, -11). 1 6. Its graph is wider than the graph of y = x2.
9-3 and 9-4 So l v i n g Q u a d r a t i c Eq u a t i o n s
Quick Review
The standard form of a quadratic equation is
a x 2 + bx + c = 0, where a + 0. Quadratic equations
can have two, one, or no real-number solutions. You can
solve a quadratic equation by graphing the related function
and finding the x-intercepts. Some quadratic equations
can also be solved using square roots. If the left side of
ax 2 + bx + c = 0 can be factored, you can use the
Zero-Product Property to solve the equation.Ex a m p l e
What are the solutions of 2x2 — 72 = 0?
2x - 72 = 0
2x2 = 72
x2 = 36Add 72 to each side.
D iv id e ea ch s id e by 2.
x = ± V36 Find th e s q u a re ro o ts o f ea ch side.
x = ± 6 Simplify.Ex e r c i se s
Solve each equation. If the equation has no real-number
solution, write no solution.- 6(x2 — 2) = 12 18. -5m 2
- 9 (> 2 + 1) = 9
- 4 = 9fc2
Solve by factoring.- x2 + 7x + 12 = 0
- 2x2 - 9x = x2 - 20
-125- 3r2 + 27 = 0
- 4rz2 = 64
- 5x2 - lOx = 0
- 2x2 + 5x = 3
- 3x2 — 5x = —3x2 + 6 28. x2 — 5x + 4 = 0
- Geom etry The area of a circle A is given by the
formula A = ttt2, where r is the radius of the circle.
Find the radius of a circle with area 16 in.2. Round to
the nearest tenth of an inch.
604 Chapter 9 Chapter Review