Question
Asked Oct 7, 2019
40 views

A parabola that passes through the point (7, -20) has vertex (-3, 10).  Its line of symmetry is parallel to the y-axis.

Find equation of the parabola:  y =  

When x = 17, what is the value of y: 

What is the average rate of change between x = -3 and x = 17:

check_circle

Expert Answer

Step 1

Given information:

A parabola that passes through the point (7,-20) and has vertex (-3,10)
Its line of symmetry is parallel to the y axis
help_outline

Image Transcriptionclose

A parabola that passes through the point (7,-20) and has vertex (-3,10) Its line of symmetry is parallel to the y axis

fullscreen
Step 2

Find the equation of the parabola as follows.

General equation of parabola in vertex form y = a(x- h) k
Where (h,k) is vertex of parabola.
It is given that the vertex (-3,10)
Therefore,
ya(x-(-3)10
y=a(x+3)+
10
Since, a parabola that passes through the point (7,-20).
- 20 %3 а(7+3)*
+10
-30 a(10)
30
100
a=-0.3
Thus the required equation is y -0.3(x +3)+
10
help_outline

Image Transcriptionclose

General equation of parabola in vertex form y = a(x- h) k Where (h,k) is vertex of parabola. It is given that the vertex (-3,10) Therefore, ya(x-(-3)10 y=a(x+3)+ 10 Since, a parabola that passes through the point (7,-20). - 20 %3 а(7+3)* +10 -30 a(10) 30 100 a=-0.3 Thus the required equation is y -0.3(x +3)+ 10

fullscreen
Step 3

Find the value of y when x...

y =-0.3(17 +3
y 0.3(400)+10
= 0.3(400)
y=12010
y =110
help_outline

Image Transcriptionclose

y =-0.3(17 +3 y 0.3(400)+10 = 0.3(400) y=12010 y =110

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus

Other