Solve using QUADRATIC FORMULA
3x^2 - 4x = -10
There is no Solution! A square root of a negative is not possible, as you would get √-104, which can only be done using "i".
x^2 - 5x = 24
The answer would be: x = -3 and x = 8. To find it, (First subtract the "24", then) use a CAB table, which will bring you the numbers: ab = -24, a + b = -5. The numbers that match would be: 3, -8. Finally, plug it in to get: x^2 - 8x + 3x - 24, then 1. x (x - 8), 2. 3 (x - 8). In the end, you can combine to form (x - 8) (x + 3), and after solving: "x = 3, x = -8"
10x^2 - 1x - 11
x = -1, x = 1.1
Identify the Vertex of this function:
Exact: (.167, 22.667)
About: (.15, 22.65)
Identify the Range of the following function:
y >= -15.769
x^2 + 8x + 16 = 0
x = -4. This is because if you plug it into the Quadratic Formula, you would get -8±√0 / 2. Since √0 = 0, you would get -8/2, which is -4.
x^2 + 6x + 8 = 0
Starting off, make a CAB table: ab = 6, a + b = 8. "a" would then be 4, and "b" would be 2. Plug it in: "x^2 + 4x + 2x + 8". Combine: x(x + 4) + 2(x + 4). Finally, it would be (x + 2) (x + 4), making "x = -4, and x = -2".
3x^2 - 12x + 5
x = .472, x = 3.528
Identify the Root of the following Function:
There are none!
What is the Range of the following function:
All real numbers.
7x^2 - 19x = 127
x = -3.113 and x = 5.828. This is because once the equation is plugged in, you will get
−(−19) ± √ 361 − (4)(7)(−127)
This can then be simplified into:
19 ± √3917 / 14 = 19 ± 60.586 / 14
Then finally:
x = 5.828, and 3.113
3x^2 - 9x - 30 = 0
First, factor out the "3" to get 3(x^2 - 3x - 10). Then, using the CAB method, find ab = -10, and then a + b = -3. "a" would then be 2, and "b" would then be -5. Combine: "x^2 - 5x + 2x - 10", and then x(x - 5), and 2(x - 5). In the end, you'd get 3([x - 5][x+2]), which is x = 5, x = -2.
3x^2 + 10x + 10
No Solutions
Identify the Axis of Symmetry in this function:
x = 0
What is the Range of the following function?
-6.9 <= y <= 6.7