Chapter 8.3, Problem 3E

To determine

Find the vertex , axis of symmetry and y - intercept from the graph.

Answer to Problem 3E

Vertex : $(2,-1)$

Axis of Symmetry : x = 2

y -intercept : (0,1)

Explanation of Solution

Given Information:

Given graph is :

  

Concept Used :

• The axis of symmetry intersects a parabola only at one point , called the Vertex.
• Axis of Symmetry: Passes through the vertex and divides the parabola into two congruent halves.
• y -intercept = The y coordinate of the point at which the graph intersects y -axis , x = 0.

Calculation:

• Find Axis of Symmetry :

  Clearly the parabola is symmetric about the line x = 2 , so , it is the axis of symmetry.

  The equation of axis of symmetry is x = 2

• Find Vertex :

  The axis of symmetry intersects the parabola at the point (2,-1).

  So, the vertex is (2,-1).

• Find y -intercept :

The y -coordinate of the point at which the graph cuts the y -axis is the y -intercept.

So, y -intercept = (0,1)