Chapter 9.3, Problem 38PPS

(a)

To determine

Graph $y=x^2$

Answer to Problem 38PPS

  

Explanation of Solution

Given:

The equation, $y=x^2$

Concept Used:

The solutions of a quadratic equation are given by the points where the graph of the function intersects the x-axis.

In order find the solutions of the given equation $y=x^2$ , first plot the graph of the function $y=x^2$ and identify the zeros of the function. The zeros of the function are the points where the graph of the function intersects the x-axis. The graph of the function $y=x^2$ is shown below,

  

(b)

To determine

The vertex and two other points on the graph

Answer to Problem 38PPS

Vertex $\left(0,0\right)$

Points

Explanation of Solution

Given:

  

In order find the vertex and two other points on the graph

Vertex points $\left(0,0\right)$

(c)

To determine

Graph $y=x^2+2,y=x^2+4,\text{and}y=x^2+6$ on the same plane

Answer to Problem 38PPS

  

Explanation of Solution

Given:

The equation, $y=x^2+2,y=x^2+4,\text{and}y=x^2+6$ .

Concept Used:

The solutions of a quadratic equation are given by the points where the graph of the function intersects the x-axis.

In order find the solutions of the given equation $y=x^2+2,y=x^2+4,\text{and}y=x^2+6$ , first plot the graph of the function $y=x^2+2,y=x^2+4,\text{and}y=x^2+6$ and identify the zeros of the function.

The zeros of the function are the points where the graph of the function intersects the x-axis.

The graph of the function $y=x^2+2,y=x^2+4,\text{and}y=x^2+6$ is shown below,

  

(d)

To determine

The vertex and two points from each of these graphs that have the same x-coordinates

Answer to Problem 38PPS

The equation is $y=x^2+2,y=x^2+4,\text{and}y=x^2+6$ we see the graph of these equations in graph increased by 2 units up to the y- axes

Explanation of Solution

Given:

The equation $y=x^2+2,y=x^2+4,\text{and}y=x^2+6$

Concept Used:

The solutions of a quadratic equation are given by the points where the graph of the function intersects the x-axis.

In order find the vertex and two points from each of these graphs that have the same x-coordinates the solutions of a quadratic equation are given by the points where the graph of the function intersects the x-axis. The equation is $y=x^2+2,y=x^2+4,\text{and}y=x^2+6$ we see the graph of these equations in graph increased by 2 units up to the y- axes

(e)

To determine

The conclusion

Answer to Problem 38PPS

The equation is $y=x^2+2,y=x^2+4,\text{and}y=x^2+6$ we see the graph of these equations in graph increased by 2 units up to the y- axes and continuously increasing towards the y-axis

Explanation of Solution

The equation is $y=x^2+2,y=x^2+4,\text{and}y=x^2+6$ we see the graph of these equations in graph increased by 2 units up to the y- axes and continuously increasing towards the y-axis

(e)

To determine

The conclusion

Answer to Problem 38PPS

The equation is $y=x^2+2,y=x^2+4,\text{and}y=x^2+6$ we see the graph of these equations in graph increased by 2 units up to the y- axes and continuously increasing towards the y-axis

Explanation of Solution

The equation is $y=x^2+2,y=x^2+4,\text{and}y=x^2+6$ we see the graph of these equations in graph increased by 2 units up to the y- axes and continuously increasing towards the y-axis