Part A:The area of a square is (4x2 − 12x + 9) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work. (5 points)
Part B: The area of a rectangle is (16x2 − 9y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)
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4x^2 -12x +9
4 x 9 = 36
first take out the LCM of 36
it will be
2 x 2 x 3 x 3
4x^2 -6x -6x +9
it is showing that
2x-3 is the length for part A
for part B
what you will do
16x^2 - 9y^2
you will use this formula here
x^2 -y^2 = (x-y) (x+y)
16x^2 -9y^2 = (4x -3y) (4x +3y)
this is the answer for part B
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I hope you get what i explain here
I do thank you so much can you help me with one more problem
An expression is shown below:
f(x) = –16x2 + 22x + 3
Part A: What are the x-intercepts of the graph of the f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)
sorry idk about this one
x intercept is when you set y=0
okay but I am still confused on how you find part b and part c
well first find the x intercepts you will get something like this
like say for example your x intercepts or "roots" or sometimes called zeros are
-3 and 4
the distance of that is 4 - (-3)=7 and half of 7 is 3.5
to get to get to the point between -3 and 4 just add 3.5 to -3 which is 1.5
and for c.
TO sketch it you'd plot the x intercepts, draw a vertical line between them and use symmetry.
Oh in part b if you found the mid point or MP of the vertex then the y coordinant of the vertex is
Now connect the points with a smooth line