Answer:
f(x) = -2x² - 8x - 2
General Formulas and Concepts:
- Order of Operations: BPEMDAS
- Expand by FOIL (First Outside Inside Last)
- Standard Form: f(x) = ax² + bx + c
- Vertex Form: f(x) = a(bx + c)² + d
Step-by-step explanation:
<u>Step 1: Define function</u>
Vertex Form: f(x) = -2(x + 2)² + 6
<u>Step 2: Find Standard Form</u>
- Expand by FOILing: f(x) = -2(x² + 4x + 4) + 6
- Distribute -2: f(x) = -2x² - 8x - 8 + 6
- Combine like terms (constants): f(x) = -2x² - 8x - 2
Answer:
the answer 61 cups of chocolate
Step-by-step explanation:
briniest please
Answer: D
Step-by-step explanation:
Only option that has a not equal inequality sign just like the graph.
Answer:
5
Step-by-step explanation:
I drew it out on a piece of paper. R is going up and down, through PQ, which is going left to right. If the ratio is 1:3, that means that for every 1 unit there is on one side, there are 3 units in the other. If R is -1 and P is -3, they are two numbers away from each other, which means that on the other side of R (to the right of R), there needs to be 6 numbers in between to make the 1:3 ratio. R is at -1, so then you would write the equation, -1+6=? The answer is 5.
-1+6=5 That is where Q would be
We'll first clear a few points.
1. A hyperbola with horizontal axis and centred on origin (i.e. foci are centred on the x-axis) has equation
x^2/a^2-y^2/b^2=1
(check: when y=0, x=+/- a, the vertices)
The corresponding hyperbola with vertical axis centred on origin has equation
y^2/a^2-x^2/b^2=1
(check: when x=0, y=+/- a, the vertices).
The co-vertex is the distance b in the above formula, such that
the distance of the foci from the origin, c satisfies c^2=a^2+b^2.
The rectangle with width a and height b has diagonals which are the asymptotes of the hyperbola.
We're given vertex = +/- 3, and covertex=+/- 5.
And since vertices are situated at (3,0), and (-3,0), they are along the x-axis.
So the equation must start with
x^2/3^2.
It will be good practice for you to sketch all four hyperbolas given in the choices to fully understand the basics of a hyperbola.