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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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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I have the answer just not the steps! Part A:(2x -3)^2 Part B:(4x+3y)(4x−3y)

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Do you know these? \[a^2-b^2=(a-b)(a+b) \\ (a+b)^2=a^2+2ab+b^2\]
Because the first shape is a square, the length and the width must be the same. So the area must be a perfect square. We need to find an expression that , when multiplied by itself, will give \(4x^2-12x+9\)Start by taking the square roots of the first and last coefficients. Can you do that?
Can you help me work it ut step by step plz
*out
What is the square root of the first term, \(4x^2\)?
2x^2?
Not quite. The square of 4 is 2, so you got that part right, but what is the square root of x^2? What can you multiply by itself to give x^2?
*square root of 4
I am confused
Do you understand that\[x \times x = x^2\]
yes
OK. So the square root of \(x^2\) is \(x\). OK with that?
oh okay.
All right. So the square root of \(4x^2\) is \(2x\). In other words\[2x \times 2x = 4x^2\]Make sense now?
Yes
OK. So now you need the square root of the last term, +9. What is it?
3
Great. With these two square roots, you have determined that the two factors must be\[4x^2-12x+9 = \left( 2x \text{ ? }3 \right)\left( 2x \text{ ? }3 \right)\]All that is left is to choose the correct sign, plus or minus. For that, look at the second term in the given trinomial. What sign does it have?
Minus.
Perfect. Then that is the sign you use in the factors. Therefore,\[4x^2-12x+9 = \left( 2x-3 \right)\left( 2x-3 \right)\]and you have your answer.
Keep in mind that this technique only works for factoring a perfect square trinomial.
Are these the answers. I have been working them out too: Part A) 4x2 − 12x + 9 4x^2 -6x -6x + 9 2x( 2x - 3) -3(2x - 3) (2x - 3)(2x-3) length of each side is 2x-3 Part B) 16x^2 − 9y^2 (4x)^2 - (3y)^2 (4x - 3y) (4x+3y) dimensions are 4x-3y, 4x+3y.
Yes, you are correct. Very well done!
Thank you!
You're welcome.
@ospreytriple can you help with 1 more?
An expression is shown below: f(x) = –16x2 + 60x + 16 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)
Part A: To find the x-intercepts, you must solve the equation \(-16x^2+60x+16=0\). Which method would you use; factoring by completing the square, or the quadratic formula?
quadratic formula?
OK. Go ahead. What do you get?
Can you refresh me on the formula.
For the general quadratic, \(ax^2 + bx + c=0\), the x-intercepts are found using\[x=\frac{ -b \pm \sqrt{b^2-4ac} }{ 2a }\]
can you help me through this one
I am really confused.
Have you used the quadratic formula before?
Just learning it.
OK. I'll help you set it up.
Okay thank you! I do have 1 request can you say like part a and like part b and part c because i will get confused and don't know what to say.
This is for Part A. If you look at the given trinomial and compare it with the general quadratic, you'll see that \(a=-16\), \(b=60\) and \(c=16\). Putting these values into the quadratic formula, you have\[x=\frac{ -b \pm \sqrt{b^2-4ac} }{2a } = \frac{ -60 \pm \sqrt{60^2-4\left( -16 \right)\left( 16 \right)} }{ 2\left( -16 \right) }\]Can you complete these calculations?
is it -5?
One second. I'm working it out...
okay ;]
Wait is it... x = 4 and x = -1/4.
Yayyyy! You got it. Those are the x-intercepts, \(x=4\) and \(x=-\frac{1}{4}\)
Yay :V. can you help with part B and C too?
Part B: Vertex a maximum or minimum? What it means is, is the parabola opening upward or downward? If the parabola opens upward, then the vertex is a minimum. If the parabola opens downward, then the vertex is a maximum.|dw:1440091745676:dw| Do you know how to tell which direction the parabola opens?
These are my answers so far are they correct? Part A.) f(x) = –16x^2 + 60x + 16 -4(x-4)(x+1/4) x-4=0 x+1/4=0 x=4 and x=-1/4 Part B.) vertex (15/8, 289/4) it is a maximum because the coeffficient of x^2 is -16 which is negative Part C.) You can graph the x intercepts and the vertex. That will give you the overall shape of the function.
OK. That saves me a lot of work. Hope I'm not wasting your time. I see in Part A you factored instead of using the quadratic formula. Parts B & C are correct. Good job>
Part c is correct?
Yes.
Oh. I wrote that down for notes rofl
Thank you!
You're welcome

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