Mathematics, 26.03.2020 15:56 amaljiiju5022

Find the vertex point, axis of symmetry, x-intercepts, and y-intercept of the
parabola below.
The equation y = x² + 3x – 18 is graphed on the set
of axes below.

Answers: 2

Show answers

Answers

Answer from: meganwintergirl

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.

Find the vertex point, axis of symmetry, x-intercepts, and y-intercept of the parabola below. The eq

Answer from: Quest

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!

Answer from: Quest

(1, –1), (16, –4), (36, –6)

step-by-step explanation:

given that the function is

$f(x) =\sqrt{x}$

this can also be written as

$y^{2} =x$

we have to graph this function and check which list of points lie on the graph

see attachment for graph:

we find that the points lying are (1,-1) (16,-4) and (36,-6)

since square root is there we find that x can only be posiitve but y can be since square root both positive and negative.

Another question on Mathematics

Mathematics, 21.06.2019 15:40

What term best describes a line and a point that lie in the same plane? a. congruent b. coplanar c. collinear d. equal

Answers: 1

Answer

Mathematics, 21.06.2019 17:30

Noor brought 21 sheets of stickers. she gave 1/3 of a sheet to each of the 45 students at recess. she wants to give teachers 1 1/2 sheets each.

Answers: 2

Answer

Mathematics, 21.06.2019 19:00

Give me the equations of two lines that have the same slope but are not parallel.

Answers: 3

Answer

Mathematics, 21.06.2019 20:00

Someone answer asap for ! the total ticket sales for a high school basketball game were $2,260. the ticket price for students were $2.25 less than the adult ticket price. the number of adult tickets sold was 230, and the number of student tickets sold was 180. what was the price of an adult ticket?

Answers: 1

Answer

You know the right answer?

Find the vertex point, axis of symmetry, x-intercepts, and y-intercept of the
parabola below.<...

Questions