**I need to find out what the vertex , axis of symmetry, maximum or minimum, and the domain and range for function f(x)=-(x-3)^2+2 HELP ME I DONT UNDERSTAND!!

Answers

Answer 1

Answer: Notice that the given equation is a parabola.

a) VERTEX
We need to find out where the parabola opens. You can predict the equation by tabulating any values of x and f(x). The table is shown:
x f(x)
_____
0 -7
1 -2
2 1
3 2
4 1
5 -3
As you plot it, the parabola opens downward. The vertex is (3,2) because that is the maximum point. The rest of the values are lesser than 2.
However, there is an easier technique to find the opening parabola and vertex rather than you plot it.

b) AXIS OF SYMMETRY
The axis of symmetry is a line that divides the parabola into two congruent halves. There is a formula for the axis of symmetry which is x = -b/2a.
Note: That is only applied if the parabola opens upward or downward and their axis of symmetry is a vertical line.
To get a and b, arrange the given equation first.
f(x) = -(x - 3)^2 + 2
= -(x^2 - 6x + 9) + 2
= -x^2 + 6x - 7 + 2
= -x^2 + 6x -5
The general form of the quadratic equation is ax^2 + bx + c. Setting a = -1, b = 6, c = -5, the axis of symmetry is
x = -6/(2*-1) = 3.

But anyway, you find it out the table above. We know that the coordinate of the vertex is (3,2). For instance, that is x = 3.

c) MAXIMUM or MINIMUM
Remember that the maximum refers to a vertex where the parabola opening downward. Otherwise, it is a minimum if the parabola opens upward. The maximum or minimum must have a certain value.
We know the answer will be a maximum. Since the axis is symmetry is a vertical line, the value for a maximum is 2.

d) DOMAIN and RANGE
Based on the given equation, the domain will be (-∞, ∞) because all values of x, the parabola continually spreads out.
The range will be (-∞, 2] because the maximum point is 2 and the rest of the values goes negative.

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Over the weekend, the All Smiles Run had 16,478 participants for the Half Marathon. The All Smiles 10K had 6,924 participants, and the 5-Mile Walk had 3,067 participants. How many more people participated in the Half Marathon than in the 10K race and the 5-Mile Walk combined?
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Answers

6924
+3067
=9991

16478
- 9991
= 6587

The answer is b.

The ground temperature at an airport is 13 °C. The temperature decreases by 7 °C for every increase of 1 kilometer above the ground. What is the temperature outside a plane flying at an altitude of 5 kilometers?The temperature outside a plane flying at an altitude of 5 kilometers is ____ c*?

Answers

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A line goes through{2,-3)and (-1, 0).slope =
Equation in point -slope form or equation in slope-intercept form

Answers

(2,-3)(-1,0)
slope(m) = (y2 - y1) / (x2 - x1)
slope(m) = (0 - (-3) / (-1 - 2) = 3/-3 = -1

y = mx + b
slope(m) = -1
use either of ur points (2,-3)...x = 2 and y = -3
now we sub and find b, the y int
-3 = -1(2) + b
-3 = -2 + b
-3 + 2 = b
- 1 = b

so ur equation is : y = - x - 1 (slope intercept form)

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Answers

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Mike wanted to purchase a bike for $285.00 andrealized the bike was on sale for 30% off. How much
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A. $85.50
B. $199.50
C. $315.00
D. $370.50

Answers

Answer:

Step-by-step explanation:

285 × .30 = 85.50

285 - 85.50 = 199.50

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