Question

Find the vertex point, axis of symmetry, x-intercepts, and y-intercept of the

Answer 1

Answer:

1) Vertex point (-1.5,-20.25)

2) axis of symmetry: x=-1.5

3) x-intercepts: (-6,0) and (3,0)

4) y-intercept: (0,18)

5) Graph in attachment.

Step-by-step explanation:

1) The given parabola has equation:

$y = {x}^{2} + 3x - 18$

We need to complete the square.

$y = {x}^{2} + 3x + {1.5}^{2} - {1.5}^{2} - 18$

$y = ( {x + 1.5)}^{2} - 20. 25$

This function is in the vertex form:

$y = a( {x - h)}^{2} + k$

where (h,k) is the vertex, x=h is the axis of symmetry.

By comparing our equation to the general vertex form:

The vertex point is (-1.5,-20.25)

2) The axis of symmetry divides the parabola into two congruent halves.

Since this is a vertical parabola, the axis of symmetry occuring at x=h is a vertical line.

The axis of symmetry is x=-1.5

3) Y-INTERCEPT.

The y-intercept is the point where the graph cross the y-axis.

At this point, the value of x is zero.

To find the y-intercept, we substitute x=0 in the equation of the parabola and simplify.

when x=0,

$y = {(0)}^{2} + 3(0) - 18 = - 18$

The y-intercept is (0,-18).

4) X-INTERCEPT

The x-intercepts are the points where the graph touches or intersect the x-axis.

To find the x-intercept, we substitute y=0.

$( {x + 1.5)}^{2} - 20.25 = 0$

Add 20.25 to both sides;

$( {x + 1.5)}^{2} = 20.25$

Take square root.

$(x + 1.5)= \pm \sqrt{20.25}$

$x = - 1.5\pm 4.5$

$x = - 1.5 - 4.5 \: \: or \: \: x = - 1.5 + 4.5$

$x = - 6 \: or \: x = 3$

The x-intercepts are(-6,0) and (3,0).

4) GRAPH

To graph this function, we can use transformation.

To graph the function,

$y = {(x + 1.5)}^{2} - 20.25$

We shift the parent quadratic function 1.5 units left and 20.25 units down.

See attachment for graph.