All categories

2 years ago

The graphs shown are of the form y = ax2. Which graph has the smallest value for a?

1 answer:

3 0

$y= x^{2}$ is a parabola (looks like the letter U).

The letter a represents the coefficient of $x^{2}$ and it controls two things (1) how wide or narrow the parabola is and (2) whether it is concave up (like a U) or concave down (like an up-side-down).

The absolute value of a (the number without the sign) controls how wide or narrow it is. If the absolute value is a fraction less than 1 the graph gets wider. The smaller the absolute value of the fraction the wider the graph gets.

If the absolute value of a is greater than 1 the graph gets narrower (it gets skinnier). The bigger the absolute value the narrower the graph.

So, if all the graphs look like a U (concave up) then the one with the smallest a is the one that is the widest.

The a also controls whether the graph is concave up or concave down. If a is negative

If a is negative the graph is concave down so any graph that is concave down has a smaller value of a than any graph that is concave up. However, if the graph is concave down the one with the smallest a would be the most narrow one.

So to find the one with the smallest a...
If they are all concave up (like a U) pick the widest one
and
If they are not all concave up pick the narrowest one that is concave down (looks like an upside down U)

You might be interested in

Robert drove at an average speed of 60 miles per hour for 6 hours. Nancy drove for 7 hours at an average speed of 56 miles per h

g100num [7]

A)1. 60/6=10
2. 56/7=8
3. 10-8=2

B)1.10
2.8
3.10+8=18

C)1. 360
2.392
3. 360+392=752

D)1. 360
2. 392
3. 360-392=-32

8 0

2 years ago

The following graph shows the cost c, in dollars, of p pounds of strawberries at a local grocery store.

lorasvet [3.4K]

Answer:

A. The ordered pair (5, 3.5) represents 5 lbs. of strawberries cost $3.50.

B. The cost per pound of strawberries is shown at (1, 0.7).

C. The relationship shown in the graph is a direct variation because as the pounds of strawberries increase, the cost also increases.

Explanation:

A. The coordinate is in (x,y). The x-axis represents the pound of strawberries and the y-axis represents the cost of the strawberries.

B. The cost for one pound of strawberries can be calculated to find the exact value of y (cost) when x is 1. The graph shows 5 lbs. of strawberries cost $3.50 so divide $3.50 by 5 lbs. to find the cost per pound of strawberries. 3.5 ÷ 5 = 0.7. On the graph, the cost for one pound of strawberries is at (1, 0.7)

C. A direct variation in a graph is shown when both x and y increase or decrease together. In this case, as the pounds of strawberries increase, the cost of the strawberries also increases.

6 0

2 years ago

For the function F defined by F(x) = x2 – 2x + 4, find F(| — 4|).

Lostsunrise [7]

F(x)=x^2-2x+4

$\\ \sf\longmapsto F(|-4|)$

$\\ \sf\longmapsto F(4)$

$\\ \sf\longmapsto 4^2-2(4)+4$

$\\ \sf\longmapsto 16-8+4$

$\\ \sf\longmapsto 8+4$

$\\ \sf\longmapsto 12$

7 0

2 years ago

What is the result of adding these two equations?<br> 4x – 4y = -2<br> –9x – 4y = -3

White raven [17]

The answer to your question 4x-4y= -2 plus -9x-4y= -3 is -5 because in order to find the result of the two equations would be to add the solutions to both of them together.

7 0

2 years ago

MathematicalUse Number Sense Duane and Mick are savingtheir money to build a tree house. Duane adds $5 to their piggybank every

Elina [12.6K]

Assuming they start saving at 0 dollars

45=total=duanesavings+micksavings
duanesavings=confusing, I will explain
mick savings =amount saves per week times number of weeks

duane saves 5 dollars every other week, aka 2.5 dollars per 1 week
DS=2.5w
MS=2w

since they save at same time and at that week, when the weeks are equal (w=w), 45 it total

DS+MS=45
2.5w+2w=45
4.5w=45
divide by 4.5 both sides
w=10

10 weeks

8 0

2 years ago