This powerpoint presentation discusses or talks about the topic or lesson Functions. It also discusses and explains the rules, steps and examples of Quadratic Functions.

1. QUADRATIC
FUNCTIONS

2. QUADRATIC FUNCTION
It is a second degree polynomial
Equation:
f(x) = ax2 + bx + c
where a, b, and c are real numbers

3. QUADRATIC FUNCTION
Vertex Form Equation:
f(x) = a(x – h)2 + k
where, a ≠ 0

4. QUADRATIC FUNCTION
Parabola
• It is the graph of the quadratic equation

5. QUADRATIC FUNCTION
If a > 0, the parabola opens upward
If a < 0, the parabola opens downward

8. y = a(x-h)2 + k
Vertex: (h,k)
Axis of Symmetry: x = h

9. GRAPHING A PARABOLA
WITH EQUATION IN VERTEX
FORM
To graph f(x) = a(x-h)2 + k
1. Determine whether the parabola opens upward or
downward. If a > 0, it opens upward. If a < 0, it opens
downward
2. Determine the vertex of the parabola. The vertex is (h,
k)

10. GRAPHING A PARABOLA
WITH EQUATION IN VERTEX
FORM
3. Find any x-intercept by replacing f(x) with 0. Solve
the resulting quadratic equation for x.
4. Find the y-intercept by replacing x with 0. Solve
the resulting equation for y.
5. Plot the intercepts and vertex. Connect these
points with a smooth curve

11. GRAPHING QUADRATIC
FUNCTIONS
1. Determine the coordinates of the vertex by finding
the x-coordinate from the formula x =
− b
2a
.
Substitute the x-coordinate into the original
quadratic function, and solve for y to determine
the y-coordinate for the vertex

12. GRAPHING QUADRATIC
FUNCTIONS
2. Determine a table of values by choosing at least
two x-values that are greater than the x-
coordinate of the vertex and two corresponding x-
values that are less than the x-coordinate of the
vertex

13. GRAPHING QUADRATIC
FUNCTIONS
3. Graph the function by plotting the vertex and the
set of ordered pairs from the table of values.
Next, connect the points with a smooth curve.