4. The Quadratic Polynomial
and the Parabola
Quadratic polynomial β ax 2 ο« bx ο« c
Quadratic function β
5. The Quadratic Polynomial
and the Parabola
Quadratic polynomial β ax 2 ο« bx ο« c
Quadratic function β y ο½ ax 2 ο« bx ο« c
6. The Quadratic Polynomial
and the Parabola
Quadratic polynomial β ax 2 ο« bx ο« c
Quadratic function β y ο½ ax 2 ο« bx ο« c
Quadratic equation β
7. The Quadratic Polynomial
and the Parabola
Quadratic polynomial β ax 2 ο« bx ο« c
Quadratic function β y ο½ ax 2 ο« bx ο« c
Quadratic equation β ax 2 ο« bx ο« c ο½ 0
8. The Quadratic Polynomial
and the Parabola
Quadratic polynomial β ax 2 ο« bx ο« c
Quadratic function β y ο½ ax 2 ο« bx ο« c
Quadratic equation β ax 2 ο« bx ο« c ο½ 0
Coefficients β
9. The Quadratic Polynomial
and the Parabola
Quadratic polynomial β ax 2 ο« bx ο« c
Quadratic function β y ο½ ax 2 ο« bx ο« c
Quadratic equation β ax 2 ο« bx ο« c ο½ 0
Coefficients β a, b, c
10. The Quadratic Polynomial
and the Parabola
Quadratic polynomial β ax 2 ο« bx ο« c
Quadratic function β y ο½ ax 2 ο« bx ο« c
Quadratic equation β ax 2 ο« bx ο« c ο½ 0
Coefficients β a, b, c
Indeterminate β
11. The Quadratic Polynomial
and the Parabola
Quadratic polynomial β ax 2 ο« bx ο« c
Quadratic function β y ο½ ax 2 ο« bx ο« c
Quadratic equation β ax 2 ο« bx ο« c ο½ 0
Coefficients β a, b, c
Indeterminate β x
12. The Quadratic Polynomial
and the Parabola
Quadratic polynomial β ax 2 ο« bx ο« c
Quadratic function β y ο½ ax 2 ο« bx ο« c
Quadratic equation β ax 2 ο« bx ο« c ο½ 0
Coefficients β a, b, c
Indeterminate β x
Roots β
13. The Quadratic Polynomial
and the Parabola
Quadratic polynomial β ax 2 ο« bx ο« c
Quadratic function β y ο½ ax 2 ο« bx ο« c
Quadratic equation β ax 2 ο« bx ο« c ο½ 0
Coefficients β a, b, c
Indeterminate β x
Roots β Solutions to the quadratic equation
14. The Quadratic Polynomial
and the Parabola
Quadratic polynomial β ax 2 ο« bx ο« c
Quadratic function β y ο½ ax 2 ο« bx ο« c
Quadratic equation β ax 2 ο« bx ο« c ο½ 0
Coefficients β a, b, c
Indeterminate β x
Roots β Solutions to the quadratic equation
Zeroes β
15. The Quadratic Polynomial
and the Parabola
Quadratic polynomial β ax 2 ο« bx ο« c
Quadratic function β y ο½ ax 2 ο« bx ο« c
Quadratic equation β ax 2 ο« bx ο« c ο½ 0
Coefficients β a, b, c
Indeterminate β x
Roots β Solutions to the quadratic equation
Zeroes β x intercepts of the quadratic function
16. The Quadratic Polynomial
and the Parabola
Quadratic polynomial β ax 2 ο« bx ο« c
Quadratic function β y ο½ ax 2 ο« bx ο« c
Quadratic equation β ax 2 ο« bx ο« c ο½ 0
Coefficients β a, b, c
Indeterminate β x
Roots β Solutions to the quadratic equation
Zeroes β x intercepts of the quadratic function
e.g. Find the roots of x 2 ο 1 ο½ 0
17. The Quadratic Polynomial
and the Parabola
Quadratic polynomial β ax 2 ο« bx ο« c
Quadratic function β y ο½ ax 2 ο« bx ο« c
Quadratic equation β ax 2 ο« bx ο« c ο½ 0
Coefficients β a, b, c
Indeterminate β x
Roots β Solutions to the quadratic equation
Zeroes β x intercepts of the quadratic function
e.g. Find the roots of x 2 ο 1 ο½ 0
x2 ο1 ο½ 0
x2 ο½ 1
18. The Quadratic Polynomial
and the Parabola
Quadratic polynomial β ax 2 ο« bx ο« c
Quadratic function β y ο½ ax 2 ο« bx ο« c
Quadratic equation β ax 2 ο« bx ο« c ο½ 0
Coefficients β a, b, c
Indeterminate β x
Roots β Solutions to the quadratic equation
Zeroes β x intercepts of the quadratic function
e.g. Find the roots of x 2 ο 1 ο½ 0
x2 ο1 ο½ 0
x2 ο½ 1
x ο½ ο±1
19. The Quadratic Polynomial
and the Parabola
Quadratic polynomial β ax 2 ο« bx ο« c
Quadratic function β y ο½ ax 2 ο« bx ο« c
Quadratic equation β ax 2 ο« bx ο« c ο½ 0
Coefficients β a, b, c
Indeterminate β x
Roots β Solutions to the quadratic equation
Zeroes β x intercepts of the quadratic function
e.g. Find the roots of x 2 ο 1 ο½ 0
x2 ο1 ο½ 0
x2 ο½ 1
x ο½ ο±1 ο the roots are x ο½ ο1 and x ο½ 1
27. Graphing Quadratics
The graph of a quadratic function is a parabola. y ο½ ax 2 ο« bx ο« c
y y
a
x x
aοΎ0
concave up
28. Graphing Quadratics
The graph of a quadratic function is a parabola. y ο½ ax 2 ο« bx ο« c
y y
a
x x
aοΎ0 aοΌ0
concave up
29. Graphing Quadratics
The graph of a quadratic function is a parabola. y ο½ ax 2 ο« bx ο« c
y y
a
x x
aοΎ0 aοΌ0
concave up concave down
30. Graphing Quadratics
The graph of a quadratic function is a parabola. y ο½ ax 2 ο« bx ο« c
y y
a
x x
aοΎ0 aοΌ0
concave up concave down
c
31. Graphing Quadratics
The graph of a quadratic function is a parabola. y ο½ ax 2 ο« bx ο« c
y y
a
x x
aοΎ0 aοΌ0
concave up concave down
c = y intercept
32. Graphing Quadratics
The graph of a quadratic function is a parabola. y ο½ ax 2 ο« bx ο« c
y y
a
x x
aοΎ0 aοΌ0
concave up concave down
c = y intercept
zeroes (roots)
33. Graphing Quadratics
The graph of a quadratic function is a parabola. y ο½ ax 2 ο« bx ο« c
y y
a
x x
aοΎ0 aοΌ0
concave up concave down
c = y intercept
zeroes (roots) = x intercepts
34. Graphing Quadratics
The graph of a quadratic function is a parabola. y ο½ ax 2 ο« bx ο« c
y y
a
x x
aοΎ0 aοΌ0
concave up concave down
c = y intercept
zeroes (roots) = x intercepts
οb
xο½
2a
35. Graphing Quadratics
The graph of a quadratic function is a parabola. y ο½ ax 2 ο« bx ο« c
y y
a
x x
aοΎ0 aοΌ0
concave up concave down
c = y intercept
zeroes (roots) = x intercepts
οb
xο½ = axis of symmetry
2a
36. Graphing Quadratics
The graph of a quadratic function is a parabola. y ο½ ax 2 ο« bx ο« c
y y
a
x x
aοΎ0 aοΌ0
concave up concave down
c = y intercept
zeroes (roots) = x intercepts
οb
xο½ = axis of symmetry Note: AOS is the average of the zeroes
2a
37. Graphing Quadratics
The graph of a quadratic function is a parabola. y ο½ ax 2 ο« bx ο« c
y y
a
x x
aοΎ0 aοΌ0
concave up concave down
c = y intercept
zeroes (roots) = x intercepts
οb
xο½ = axis of symmetry Note: AOS is the average of the zeroes
2a
vertex
38. Graphing Quadratics
The graph of a quadratic function is a parabola. y ο½ ax 2 ο« bx ο« c
y y
a
x x
aοΎ0 aοΌ0
concave up concave down
c = y intercept
zeroes (roots) = x intercepts
οb
xο½ = axis of symmetry Note: AOS is the average of the zeroes
2a
vertex x value is the AOS
39. Graphing Quadratics
The graph of a quadratic function is a parabola. y ο½ ax 2 ο« bx ο« c
y y
a
x x
aοΎ0 aοΌ0
concave up concave down
c = y intercept
zeroes (roots) = x intercepts
οb
xο½ = axis of symmetry Note: AOS is the average of the zeroes
2a
vertex x value is the AOS
y value is found by substituting AOS into the function.
40. Graphing Quadratics
The graph of a quadratic function is a parabola. y ο½ ax 2 ο« bx ο« c
y y
a
x x
aοΎ0 aοΌ0
concave up concave down
c = y intercept
zeroes (roots) = x intercepts
οb
xο½ = axis of symmetry Note: AOS is the average of the zeroes
2a
vertex x value is the AOS
y value is found by substituting AOS into the function.
(It is the maximum/minimum value of the function)