Quadratics
Would this parabola (-2x^2+6x-9) be concave up or down? How can you tell?
Down because of the negative sign in front of A.
What is the square root of -18?
The first step is turning the square root of -18 into 18i because nothing times itself equals a negative number. That's also the last step. If you thought there were more, I'm disappointed in you.
Using the Product Rule of Exponents, this equation simplifies into 16a^3b^2
What is the x coordinate of the axis of symmetry of -3x^2+54x-18
The axis of symmetry always passes through the middle of a parabola where the vertex is. Therefore, to find its coordinates you can use the equation -b/2(a) to find the coordinates of your axis of symmetry.
Hello, Detective Pikachu. Your mission is to simplify the equation of the square root of √-2*√-32. (Note: don't overthink it as I did. It's simpler than it may seem).
The first step is to find the common factors of 32!
32=2*2*2*2*2
This leaves you with 4√2i * √2i
Then you can use the rule √a*√a=a
In the end you get left with 4(-2)=-8
Simplify (4m^-1n^2)^3
Using the Power Rule for Exponents, we can use the distributive property to multiply the exponents of variables and square the numbers. It leaves you with:
64n^6m^-3
However, our negative exponent rule tells us that the m^-3 can be simplified by bring it to the denominator of a fraction, and removing the negative sign.
64n^6 over m^3
Find the vertex of the function 2x^2-16x+1
The vertex is...
(4,-31)
Link...LINK!! It's me, Lord Sonic from that other Nintendo universe. I have come to warn you of a great danger that threatens your dearest Zelda. To save her, you must solve the equation √-2 * √-32. If you get it wrong....SHE DIES (don't ask how :) ).
DID YOU SAVE ZELDA?? WELL, YOU SHOULD HAVE IF YOUR ANSWER WAS 8i!!! The first step to solving this equation is, well, SIMPLIFYING -2 and -32 TOOOO 2i AND 32i. Next, see if you can factor out either of them. We know that we can't factor out 2i anymore because it's only factors left are 1 and 2. However, you can factor out 32i into 2^5!. That has no square root, but 2^4 does, so we simplify the equation into √2^4 *2. Then simplify them, which leaves us with 2^2 or 4! The full problem now equals 4*√2i*√2i. But do you know what we can do to simplify further???? We can put both 2is under the same square root and combine them into 2i^2! Then, you can square root it and simplify it into 2i! That leaves you with 4*2i=8i. If you got that, then you're a good husband, wife or partner :)
Do you feel confident? Let's see if we can end that.
Using the Quotient Rule of Exponents we know that when dividing numbers with exponents that have the same base, we can subtract the exponents.
This leaves us with...
2yx^-1 times x^6
Using the Product Rule, we simplify the rest.
2yx^5
How confident are you now :)
Given the function -5x^2+50x-9, find the vertex, one point of symmetry (at least), and the y-intercept.
The vertex is (10,-9)
The point of symmetry is (11,-64)
The y-intercept is -9
Riddle me this Batman...If quizzes are quizzical...then what are tests?? Also, simplify the equation √-12*√-3*√-4. Based on previous questions, this shouldn't be too difficult, Batman. MUHUHAHAHAHA. If you don't solve this one correctly...I might just have to tear gas the whole city (cracks a sly smile).
The first step is to simplify all of them into their imaginary number forms leaving you with:
√12i*√3i*√4i
Next find the greatest common factors of each
12= 2*2*3
3=none
4=2*2
Simplify
2√3i*√3i*4i
Next you move 3i under the same square root and they cancel out the square root
2(3i)*√4i
Now, what you can do is separate the i and the 4 to create to separate square root problems.
2(-3)√i*√4
We know that the square root of 4 is 2 and that the square root of i is just i. Which leaves us with
2(-3)*i*2
Now simplify
-6i*2= -12i
Hello there! I'm here to make you feel bad about yourself. To do that, I'll give you an equation that you must simplify before anyone else. That equation is:
2yx^-1 times (x^2)^3
Using the Power to a Power Rule, simplify what everything in the parenthesis. Then, you'll be left with:
2yx^-1 times x^6
Now use the Product Rule to simplify!
Answer: 2yx^5
Did your team get it right? If so, feel bad about yourself because you're NERDS. If you lost this round, recognize that the other teams are just nerds, and you're cool as hell.
You're given the equation 1/3(x-9)(x+3). Using what you've learned, convert it into a standard form quadratic equation and solve for the vertex. Next, find one point of symmetry.
Vertex: (3,-12)
Point of symmetry: (4,11.6)
Do you ever wonder why sometimes there is no soap in one of the boy's bathrooms? Well, there are two reasons. One, because some of the kids at our school are annoying as hell, and two, because -√-75.
The first step, find the common factors of 75.
75= 3*5*5
-√ -3*-5*-5
Next, you can use the rule √a*√a=a to simplify √-5*-5 which gives you...
-5i√3i
3u^4v^2 times 3u^3v^4 over u^4v^2
Product Rule to simplify the top into
9u^7v^6 over u^4v^2
Now, use the Quotient Rule of Exponents to simplify it into this:
9u^3v^4