Step: 1

Make a table of ordered pairs for the given function.

Step: 2

Plot these points on the coordinate plane and connect the points with a smooth curve.

Step: 3

The graph looks like the one below:

Step: 4

It can be observed from the graph that the parabola opens upward.

Step: 5

The equation of the axis of symmetry is: x = 0.

Step: 6

The vertex is at (0, 0).

Step: 7

The parabola opens up. So the vertex is the minimum point.

Correct Answer is : Graph 2; opens up; x = 0; (0, 0); Minimum point

Step: 1

[Original quadratic function.]

Step: 2

[Comparing with y = ax ^{2} + bx + c .]

Step: 3

The x -coordinate of the vertex = - b 2 a = - 0 2 ( - 1 ) = 0

Step: 4

The values of y = - x ^{2} + 1 for the x -values to the left and right of x = 0 are tabulated below:

Step: 5

Plot the points and join them with a smooth curve as shown.

Step: 6

The graph matches with Graph 2.

Correct Answer is : Graph 2

Step: 1

[Original quadratic function.]

Step: 2

[Comparing with y = ax ^{2} + bx + c .]

Step: 3

The x -coordinate of the vertex = - b 2 a = - 0 2 ( 1 4 ) = 0

Step: 4

The values of y = (x 2 4 ) - 2 for the x -values to the left and right of x = 0 are:

Step: 5

Graph 3 satisfies the above table.

Correct Answer is : Graph 3

Step: 1

[Original function.]

Step: 2

[Comparing with y = ax ^{2} + bx + c .]

Step: 3

The x -coordinate of the vertex = - b 2 a = - 0 2 ( - 1 ) = 0

Step: 4

The values of y = - x ^{2} for the x -values to the left and right of x = 0 are tabulated below:

Step: 5

Plot the points and join them with a smooth curve as shown.

Step: 6

The graph matches with Graph 4.

Correct Answer is : Graph 4

Step: 1

[Original quadratic function.]

Step: 2

[Comparing with y = ax ^{2} + bx + c .]

Step: 3

The x -coordinate of the vertex = - b 2 a = - 0 2 ( 1 ) = 0

Step: 4

The values of y = x ^{2} - 1 for the x -values to the left and right of x = - 1 are tabulated below:

Step: 5

Plot the points and join them with a smooth curve as shown.

Step: 6

The graph matches with Graph 4.

Correct Answer is : Graph 4

Step: 1

[Original quadratic function.]

Step: 2

[Comparing with y = ax ^{2} + bx + c .]

Step: 3

The x -coordinate of the vertex = - b 2 a = - 5 2 ( 1 ) = - 2.5

Step: 4

The values of y = x ^{2} + 5x - 2 for the x -values to the left and right of x = - 2.5 are:

Step: 5

Graph 2 satisfies the above table.

Correct Answer is : Graph 2

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