Chapter 9.1, Problem 33PPS

To determine

To Find:

The vertex , axis of symmetry and y − intercept.

Answer to Problem 33PPS

Vertex : (0,0)

Axis of Symmetry : x = 0

y-intercept : 0

Explanation of Solution

Given Information:

Given graph is :

  

Concept Used :

• Quadratic Functions:
• Quadratic functions are non-linear and are of the form:

  $f(x)=a{x}^2+bx+c;a\ne 0$

This is the standard form of Quadratic function.

• Shape of the graph of a Quadratic function is called Parabola.
• Parabolas are symmetric about a central line called Axis Of Symmetry.
• The axis of symmetry intersects a parabola only at one point , called the Vertex.
• Parent Function:

  $y=x^2$

• Standard Form :

  $f(x)=a{x}^2+bx+c;a\ne 0$

• Type of Graph:

Parabola

• Axis of Symmetry: Passes through the vertex and divides the parabola into two congruent halves.

  $x=-\frac{b}{2a}$

• y-intercept = The y coordinate of the point at which the graph intersects y-axis = c
• Graph:

  

• If a > 0 ,
• The graph of $a{x}^2+bx+c$ opens upward.
• The lowest point on the graph is the minimum.
• If a < 0 ,
• The graph of $a{x}^2+bx+c$ opens downward.
• The highest point on the graph is the maximum.
• The maximum or the minimum is the vertex.

Calculation:

• Find the Vertex :
• Because the parabola open downward, the vertex is located at the maximum point of the parabola.
• It is located at (0,0)
• Find the Axis of Symmetry :
• The axis of symmetry is the line that passes through the vertex and divides the parabola into two congruent halves.
• It is located at x = 0.
• Find the y − intercept :
• y − intercept is the y coordinate of the point where the graph intersects the y-axis.
• It is located at (0,0).
• So , the y − intercept is 0.