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# A few questions I'm really stuck on

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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
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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
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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
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you better be sorry

Jun 24, 2019
#4
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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   Jun 24, 2019
edited by CPhill  Jun 24, 2019
#5
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Sorry for all these questions XD Plz forgive me XD. But thanks :)

Jun 25, 2019