Given
y=x²+4x+3
find the vertex,
focus and
directrix
Answers
Answer:
Step-by-step explanation:
The given y=x²+4x+3 should be re-written in "vertex form," which is
y = a(x - h) + k, where (h, k) is the vertex.
Here y=x²+4x+3 = y=x²+4x + 4 - 4 +3 (completing the square), or
y = x^2 + 4x + 4 - 1. which condenses to y = (x + 2)^2 - 1
Thus, h = -2 and k = 1, and so the vertex is at (h, k), or (-2, 1). This parabola opens up. The axis of symmetry is the vertical line x = -2.
An alternative equation for a vertical parabola that opens up is:
y - k = 4p(x - h)^2. Rewriting y = (x + 2)^2 - 1 to fit this form leads to:
y + 1 = 4p(x + 2)^2. We must find the value of p that makes this equation true at any (x, y) on the graph. Suppose we arbitrarily choose x = 1. Then, according to y=x²+4x+3, y = 1^2 + 4(1) + 3, or y = 8 when x = 1.
Then y - k = 4p(x - h)^2 becomes 8 - 1 = 4p(1 + 2)^2, or
7 = 4p(9), or p = 7/36
The focus is thus 7/36 units above the vertex: (-2 + 7/36), and the directrix is the horizontal line which is 7/36 units below the vertex: y = -2 - 7/36.
Vertex: (-2, 1)
Focus: (-2, 2 7/36)
Directrix: y = -2 7/36
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Answer: Evaporate the water by boiling it in a pot with a lid or another container. This separates both substances as the boiling point for water is much lower than salt, this method is called simple distillation.
Answer:
Salt is ionic, and oil is covalent. If you add water, the salt will dissolve in the water, and the oil will float to the top. You could then skim the oil and start over with sugar. To double-check, you could even make sure the oil does not conduct electricity!
Step-by-step explanation:
Answers
=> 2
Answer:
(x + 2)(2x + 1)
Step-by-step explanation:
Hello!
We can factor this expression using the grouping method.
What is the Grouping Method?
The grouping method is a way to factor quadratic expressions and is mostly likely used when given an even number of terms. I will show you how to factor by grouping shortly.
Step 1: AC and B
This equation is written in the standard form of a quadratic : ax² + bx + c
The rule of grouping is that we need to find two factors, so that when the terms ax² and c are multipliedd together, the two factors would add to bx.
Using the given problem:
- ax² is 2x²
- bx is 5x
- c is 2
Multiply:
- 2(2x²)
- 4x²
That means that the two factors that multiply to 4x² should add to 5x. The terms that work is x and 4x.
Step 2: Expand and factor
Now we simply replace 4x and x for 5x.
- 2x² + x + 4x + 2
Now think of these one expressions as two seperate ones.
- (2x² + x) + (4x + 2)
Find the GCF in both parenthesis
- x(2x + 1) + 2(2x + 1)
Simplify
- (x + 2)(2x + 1)
Your factored equation is (x + 2)(2x + 1)
Answers
Answer:
14 +3 - 17
6-4 = 2
1 -9 = -8
Step-by-step explanation:
Answer:
14+3= 17
6-4= 2
1 -9= -8
Step-by-step explanation:
Answers
Answer:
Supplementary
Step-by-step explanation:
Both angles are consecutive interior angles. These are interior angles formed within the inner region of the two parallel lines. Therefore they are supplementary.
Answers
Answer:
His speed in miles per minute
Step-by-step explanation: