C. multiplication (the 8 x 9 within the parenthesis)
Answer:
Horizontal shift of 4 units to the left.
Vertical translation of 8 units downward.
Step-by-step explanation:
Given the quadratic function, y = (x + 4)² - 8, which represents the horizontal and vertical translations of the parent graph, y = x²:
The vertex form of the quadratic function is y = a(x - h)² + k
Where:
The vertex is (h , k), which is either the <u>minimum</u> (upward facing graph) or <u>maximum</u> (downward-facing graph).
The axis of symmetry occurs at <em>x = h</em>.
<em>a</em> = determines whether the graph opens up or down, and makes the graph wider or narrower.
<em>h</em> = determines how far left or right the parent function is translated.
<em>k</em> = determines how far up or down the parent function is translated.
Going back to your quadratic function,
y = (x + 4)² - 8
- The vertex occrs at (-4, -8)
- a is assumed to have a value of 1.
- Given the value of <em>h</em> = -4, then it means that the graph shifted horizontally by <u>4 units to the left</u>.
- Since k = -8, then it implies that the graph translated vertically at <u>8 units downward</u>.
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Answer:
Step-by-step explanation:
We are asked to divide our given fraction: 
.
We will simplify our division problem using rules of exponents.
Using product rule of exponents 
we can write:
Substituting these values in our division problem we will get,
Using power rule of exponents 
we will get,
Using quotient rule of exponent 
we will get,
Using product rule of exponents we will get,
Upon canceling out 
we will get,
Using power rule of exponents we will get,
Therefore, our resulting quotient will be .
9514 1404 393
Answer:
(c) P(x) = x^4 +3x^3 -10x^2 -30x
Step-by-step explanation:
If the polynomial has integer coefficients, its complex or radical roots come in conjugate pairs. That is, -√10 is also a root. The four roots mean the polynomial has degree 4. That eliminates all but answer choice C.
Each root 'a' gives rise to a factor (x -a), so the factored polynomial is ...
P(x) = (x -0)(x -(-3))(x -√10)(x -(-√10))
P(x) = x(x +3)(x² -10) = x(x³ +3x² -10x -10)
P(x) = x^4 +3x^3 -10x^2 -10x
Answer:
4.33
Step-by-step explanation:
1/3=0.33 recuring
4 just eqauls 4
so you add 0.3 recuring to 4
and depending on significant figures it wants you round it ill assume it wants 3 and go 4.33
