Chapter 9.1, Problem 71HP

To determine

To Find:

Another point on the graph. Explain how you found it.

Answer to Problem 71HP

Another point on the graph is (-1,9).

Explanation of Solution

Given Information:

The graph of a quadratic function has a vertex at (2, 0). One point on the graph is (5, 9).

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.
• 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:

• The vertex of the graph is (2,0).
• Since the axis of symmetry passes through the vertex , so the equation of axis of symmetry is x = 2.
• Plotting points (2,0) and (5,9) and drawing the upward parabola:
• 
• From the graph, since the axis of symmetry cuts the parabola into two congruent halves.
• First , we count the units to move right and up from the vertex to the point (5,9). We have to move 3 units right and then 9 units up to reach (5,9) from (2,0).
• So, due to symmetry of the axis of symmetry, we will move 3 units to the left and then 9 units up from (2,0) , the vertex. We reach the point (-1,9).
• So, another point on the graph is (-1,9)