Answer:
f(x) = 4x^2 + 2x - 4.
Step-by-step explanation:
Let the quadratic function be y = f(x) = ax^2 + bx + c.
For the point (-2, 8) ( x = -2 when y = 8) we have:
a(-2)^2 + (-2)b + c = 8
4a - 2b + c = 8 For (0, -4) we have:
0 + 0 + c = -4 so c = -4. For (4, 68) we have:
16a + 4b + c = 68
So we have 2 systems of equations in a and b ( plugging in c = -4):
4a - 2b - 4 = 8
16a + 4b - 4 = 68
4a - 2b = 12
16a + 4b = 72 Multiplying 4a - 2b = 12 by 2 we get:
8a - 4b = 24
Adding the last 2 equations:
24a = 96
a = 4
Now plugging a = 4 and c = -4 in the first equation:
4(4) - 2b - 4 = 8
-2b = 8 - 16 + 4 = -4
b = 2.
Answer:

General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS<u>
</u>
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Coordinates (x, y)
- Slope Formula:

Step-by-step explanation:
<u>Step 1: Define</u>
Point (2, 5)
Point (-3, 7)
<u>Step 2: Identify</u>
x₁ = 2, y₁ = 5
x₂ = -3, y₂ = 7
<u>Step 3: Find slope </u><em><u>m</u></em>
Simply plug in the 2 coordinates into the slope formula to find slope<em> m</em>
- Substitute in points [Slope Formula]:

- [Slope] [Fraction] Subtract:

- [Slope] [Fraction] Rewrite:

Answer:
3:4
Step-by-step explanation:
(1/7)/(4/21) = (1/7)×(21/4) = 3/4 = 3:4
Answer:
D: -5(-6x^2 + x + 2)
E: 5(2x + 1)(3x − 2)
Step-by-step explanation:
The <em>first two answer choices have incorrect constants</em> (25 and 3 vs -10). A factor of 5 is removed from the remaining answer choices, so let's remove a factor of 5 and see what we get:
30x^2 -5x -10 = 5(6x^2 -x -2)
An additional x cannot be factored from the expression, so <em>choice C can be eliminated</em>.
Multiplying each of these factors by -1 will make the product correspond to answer choice D.
Factoring will make it correspond to answer choice E, best verified by finding the x-term of the product of the binomial factors:
E: 2x(-2) +1(3x) = -x, as required
F: 2x(2) -1(3x) = x, wrong sign
The equivalent expressions are those of choices D and E.
Answer:
8/7
Step-by-step explanation:
0.8/0.7=8/7