 ## Presentation on theme: "2.1 – Quadratic Functions."— Presentation transcript:

In this section, you will learn to
analyze graphs of quadratic functions write quadratic functions in standard form and sketch its graphs solve real-life problems

Definition of a Polynomial Function:

a) Axis of symmetry: the line where the parabola is symmetric b) Vertex: The point where the axis of symmetry intersects the parabola

c) Upward or Downward: If the leading coefficient is positive (a>0) , the parabola opens upward.

c) Upward or Downward: If the leading coefficient is negative (a<0) , the parabola opens downward.

d) Minimum or Maximum: If the parabola opens upward, the vertex has a minimum value. If the parabola opens downward, the vertex has a maximum value.

Standard Form of a Quadratic Function:
a) Vertex: b) Axis of Symmetry: c) Vertex: Therefore, * To write an equation in standard form, you need to complete the square.

Identify the vertex and axis of symmetry for
There are two methods to identify the vertex and the axis of symmetry. Method 1:

Method 2: Complete the Square

Complete the Square:

Method 2: Complete the Square

Identify the vertex and zeros to graph:

Identify the vertex and zeros to graph:
Vertex: Zeros:

Find the quadratic equation in standard form:

Find the quadratic equation in standard form:
Vertex: Point:

Real-Life Example:

Real-Life Example: Since this parabolic path is opening downward, the maximum height is reached at the vertex point. You can use the formulas for h and k to find the vertex point. Then, the maximum height is represented by the k value.

Real-Life Example: The maximum height reached by this ball is 130 ft.

Graph: The maximum height reached by this ball is 130 ft.

Real-Life Example:

Real-Life Example: Since this parabolic path is opening upward, the minimum height is reached at the vertex point. You can use the formulas for h and k to find the vertex point. Then, the minimum height is represented by the k value.

Real-Life Example: The minimum height reached by the yo-yo is 16 feet.

Real-Life Example: The minimum height reached by the yo-yo is 16 feet.