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1. Consider the parabola y=-5x^2+17x-12 . What is the vertex of this parabola?

 

2. What is the equation of the line of symmetry of the parabola y=-5x^2+17x-12

 

3.What are the x-coordinate(s) of all point(s) where the parabola y=-5x^2+17x-12 intersects the line y=0?

 

4. For what values of x  is -5x^2+17x-12 negative?

 

Sorry for all of these...

 Jun 24, 2019
 #1
avatar+45 
+1

1. (1.7, 2.45)

2. x = 1.7

3. (1,0) and (2.4,0)

4. (2.45, negative infinity)

 Jun 24, 2019
edited by Guest  Jun 24, 2019
 #2
avatar+45 
+1

1. use the formula of line of symetry to find x cordanite: -b/2a

2. When you find what -b/2a is, plug it into the formula

3. set the equation to zero and find the roots

4. since the parobla has max, it is (2.45, -infinity)

DungeyDabs  Jun 24, 2019
 #3
avatar+45 
-1

you better be sorry

 Jun 24, 2019
 #4
avatar+103069 
+2

1. Consider the parabola y = -5x^2+17x-12 . What is the vertex of this parabola?

 

We have the form Ax^2 + Bx + C

 

The x coordinate of the vertex  is given by   -B / [2A]  =  -17/ [ 2(-5)]  =  17/10

 

Put this value back into the function to get the y coordinate of the vertex 

 

-5(17/10)^2 + 17(17/10) - 12  =

-5 (289/100) + 289/10 - 12   =   49/20

 

So.....the vertex  is  ( 17/10, 49/20)

 

 

2. What is the equation of the line of symmetry of the parabola y=-5x^2+17x-12

 

Easy.....the  equation for the symmetry line is 

x  = x coordinate of the vertex

So....   x  = 17/10

 

3.What are the x-coordinate(s) of all point(s) where the parabola y=-5x^2+17x-12 intersects the line y=0?

We need to solve this

-5x^2 + 17x - 12  =  0     factor as

(-5x + 12) ( x - 1)  = 0

Set each factor to 0  and solve for x   and we have that

-5x + 12 = 0            x  - 1  = 0

12 = 5x                    x = 1

12/5 = x        

 

 

4. For what values of x  is -5x^2+17x-12 negative?

The parabola has its vertex above the x axis  and it turns downward because of the -5 in front of the x^2 term

It will intersect the x axis at  x = 1  and x  = 12/5

So......it will be negative from  (-infinity , 1)  and from (12/5, infinity)

See the graph here : https://www.desmos.com/calculator/visfr9nhfz

 

 

 

 

 

cool cool cool

 Jun 24, 2019
edited by CPhill  Jun 24, 2019
 #5
avatar+91 
+1

Sorry for all these questions XD Plz forgive me XD. But thanks :)

 Jun 25, 2019

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