powerpoint presentation

1. Graph ofQuadraticFunction
Ms. G. Martin

2. Contoso
S u i t e s
2
A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b,
and c are numbers with a not equal to zero. The graph of a quadratic function is a
curve called a parabola. Parabolas may open upward or downward and vary in
"width" or "steepness", but they all have the same basic "U" shape.
The graph opens downward if a > 0 and downward f a < 0.
Vertex - The point where the parabola intersects its axis of symmetry and is the
point where the parabola is most sharply curved.
- It is also the turning point of the graph. We can see that the vertex is at
(3,0) .

3. Contoso
S u i t e s
3

4. Contoso
S u i t e s
4
Axis of symmetry - is the vertical line
that intersects the parabola at
the vertex.
It is a vertical line that divides the
parabola into two congruent halves.
The x -coordinate of the vertex is the
equation of the axis of symmetry of
the parabola or represented by the
formula h = -
𝒃
𝟐𝒂
.

5. Contoso
S u i t e s
5

6. Contoso
S u i t e s
6
How to graph Quadratic Function
So, to get the vertex form of
the quadratic function use
the formula of
h(x) = -
𝒃
𝟐𝒂
and
k = f(h) or k(y) = (-
b2 – 4ac
4a
)

7. Contoso
S u i t e s
7

8. Contoso
S u i t e s
8
Or use the formula of h and k,
where h is the value of x and k is
the value of y.
h = -
𝒃
𝟐𝒂
= -
𝟏𝟐
𝟐(𝟏)
= -6
= -
b2 – 4ac
4a
= -
122 – 4(1)(32)
4(𝟏)
= -
𝟏𝟒𝟒 −𝟏𝟐𝟖
𝟒
= -
𝟏𝟔
𝟒
= -4
So, the vertex(h, k) is (-6, -4)