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Thank you! (For (d) you don't have to graph it on a coordinate plane if it's too inconvenient, please just explain where I need to graph!)

 Apr 23, 2021
 #1
avatar+1300 
+2

Hello!

 

You can graph it out with desmos. https://www.desmos.com

x intercepts are when y = 0, when y = 0, the x coordinates are -4 and 1. 

y intercepts are when x = 0, which is 4. 

https://www.varsitytutors.com/hotmath/hotmath_help/topics/axis-of-symmetry-of-a-parabola

Try to see if you can find the vertex and axis by yourself. :))

You can also see by graphing it in desmos. 

 

=^._.^=

 Apr 23, 2021
 #2
avatar+79 
+1

Thanks so much for the explanation and references, it really helps! :)

Corduroy  Apr 23, 2021
 #3
avatar+1300 
+1

You're welcome :)

 

=^._.^=

catmg  Apr 23, 2021
 #4
avatar+79 
+1

Hi again!

 

I spent some time trying to solve this problem but I am a little confused. Could you show me how you got the x and y intercepts? I'm not sure how you got to -4 and 1. I'm sorry I'm new to this :(

Corduroy  Apr 24, 2021
 #5
avatar+113177 
+2

Hi Cordueroy,  catmg has given you a good answer but I am happy to discuss it with you.

 

This question is poorly written because the formula has f(x) but you are asked for y.

You just need to understand that  y=f(x)

 

 

\(f(x)=-(x+4)(x-1)\)

 

Think about the y axis, what are some points on the y axis? 

(0,6), (0,-2) (0,7) .... etc,    What do they all have in common?   well the x value is always 0.

SO,  the equation of the y axis is  x=0

So to find the y intercept, that is where it crosses the y axis, you must solve the equation simultaneously with x=0.

that might sound complicated but it is not.

Just substitute the x in the equation with 0,  like this

\(f(0)=-(0+4)(0-1)\\ f(0)=-+4*-1\\ f(0)=+4 \)

 

So the y intercept (which should really be called the f(x) intercept) is 4

-----------

the x axis has the equation y=0     f(x)=0

To find the x intercept you have to solve   

 

\(0=-(x+4)(x-1)\)

 

Two terms will only multiply to give 0 if one or both of them is equal to 0 so

either       

\(x+4=0\quad \rightarrow \quad x=-4\\or\\ x-1=0\quad \rightarrow \quad x=+1\)

 

so the x intercepts are   -4 and 1

 

-----------------------------------------------

This is a concave down parabola. 

I know that it is a parabola because  the highest power of x, if you multiply it out is 2     (x^2) 

And I know it is concave down because it will because the leading coefficient is neg    (-x^2)

 

The axis of symmetry for a parabola, concave up or down, is half way between the two x intercepts 

\(x=\frac{-4+1}{2}=\frac{-3}{2}=-1.5\)

 

The equation of the axis of symmetry is x = -1.5

---------------------------------------------------

 

To find the vertex, substitute x=-1.5 into the formula to find the y value.

 

------------------------------------------------

 

And as catmg already suggested, use  Desmos to graph it.  wink

 

https://www.desmos.com/calculator

 Apr 24, 2021
edited by Melody  Apr 24, 2021
 #6
avatar+79 
+1

This was a great explanation! Your explanation and catmg's explanations help immensely, thank you!

Corduroy  Apr 24, 2021
 #7
avatar+113177 
0

Thanks Corderoy,  I am glad I could help.

Melody  Apr 25, 2021

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