This document discusses quadratic functions and equations involving one variable with the highest power being 2. It defines quadratic expressions and determines whether expressions are quadratic. It covers determining the values of a, b, and c for quadratic expressions. It discusses key features of quadratic functions including the turning point (maximum/minimum), the coordinate of the turning point, the y-intercept, x-intercepts, and the equation of the axis of symmetry. Examples are provided to illustrate these concepts and have students practice identifying these features from graphs and expressions.

1. QUADRATIC FUNCTIONS AND
EQUATIONS IN ONE VARIABLE
4 AMBER

2. **Involves one variable with the highest power of 2
Example:
Quadratic
expression
Variable Highest power
of variable
𝑥2
+ 2𝑥 − 1
−𝑦2
+ 3𝑦
𝑚2
− 𝑚 + 4
2𝑛2
+ 5

3. Determine whether each of the following
expression is a quadratic expression in one variable.
Expression Variable Highest
power of
variable
Is it a
quadratic
expression?
3𝑦2
− 3𝑥 − 1
−𝑦3
+ 3𝑦
−
1
2
𝑚2
2𝑛2
+ 5

4. Expression Variable Highest
power of
variable
Is it a
quadratic
expression
𝑥
1
2 + 2𝑥 − 1
2𝑦2
+ 𝑦−2
1
𝑥2
+ 4x − 1

5. Determine the values of a , b and c for each of the following quadratic
expressions.
a) 2𝑥2
− 5𝑥 + 1
b) 𝑥2
− 2𝑥

6. c) 2𝑦2 + 1
d) −
1
2
𝑝2
+ 4𝑝

7. Turning
point
Turning point
(Maximum point or
minimum point)
Coordinate of
turning point
y-intercept, c
x-intercept
Equation of axis of
symmetry

8. Turning point
(Maximum point or
minimum point)
Coordinate of
turning point
y-intercept, c
x-intercept
Equation of axis of
symmetry

9. Turning point
(Maximum point or
minimum point)
Coordinate of
turning point
y-intercept, c
x-intercept
Equation of axis of
symmetry

10. a) 𝑦 = 2𝑥2
+ 4𝑥 + 1
𝒙 𝒇 𝒙 = 𝑦 = 2𝑥2
+ 4𝑥 + 1 (𝒙. 𝒚)
−3 2(−3)2+4 −3 + 1 = 7 (-3, 7)
−2
−1
0
1

12. 𝑓 𝑥 = 2𝑥2
+ 4𝑥 + 1
-3
-2
-1
0
1
-1
1
7
𝑥 𝑦
Object Image

13. b) 𝑦 = −𝑥2
+ 3
𝒙 𝒇 𝒙 = 𝑦 = −𝑥2
+ 3 (𝒙. 𝒚)
−3 −(−3)2
+3
−2
−1
0
1
2
3

15. 𝑓 𝑥 = −𝑥2
+3
-3
-2
-1
0
1
2
3
-6
-1
2
3
𝑥 𝑦
Object Image

16. Indicate the shape of the graphs by putting either a smile on
the face, or an unhappy gesture if otherwise.
a) 𝑓 𝑥 = 𝑥2 + 𝑥 − 2
b) 𝑓 𝑥 = −𝑥2
+ 4𝑥 + 3

17. c) 𝑓 𝑥 = 3 + 5𝑥 − 3𝑥2
d) 𝑓 𝑥 = 1 + 4𝑥 − 4𝑥2

18. Determine the maximum or minimum point.
Draw and state the axis of symmetry.
1) Turning point
(Maximum point or
minimum point)
Coordinate of
turning point
Equation of axis of
symmetry

19. 2)
Turning point
(Maximum point
or
minimum point)
Coordinate of
turning point
Equation of axis of
symmetry

20. Determine the value of 𝒄 from the quadratic
function.
Determine the value of 𝒄 from the graph quadratic
function.
1)

21. 2)
From the graph of quadratic function
From quadratic function

22. 3)
From quadratic function From the graph of quadratic function

23. Self practice 1.1 c Textbook Page 14
1. The quadratic functions below pass through the
points stated. Calculate the value of c for each case.
(a)f(x) = 𝑥2
+ 7𝑥 + 𝑐, passes through point (0, 5).
(b)f(x) = 2𝑥2
− 7𝑥 + 𝑐, passes through point (2, –3).
(c)f(x) = −2𝑥2
+ 𝑥 + 𝑐 , y-intercept = 4.