## Tuesday, January 24, 2023

### Algebra Problems of the Day (Algebra 1 Regents, August 2022)

The following questions appeared on the August 2022 Algebra 1 Regents Exam

More Regents problems.

### Algebra 1 Regents, August 2022

11. What would be the order of these quadratic functions when they are arranged from the narrowest graph to the widest graph?

f(x) = -5x2, g(x) = 0.5x2, h(x) = 3x2

1) f(x), g(x), h(x)
2) g(x), h(x), f(x)
3) h(x), f(x), g(x)
4) f(x), h(x), g(x)

Ignore the sign of the coefficient. We only care about how big that value is absolutely. The narrowest graph with have the largest coefficient (absolutely) making it jump higher faster. The closer the coefficient is to 0, the wider it will be.

So |-5| > |3| > |0.5|, makined f(x) the narrowest and g(x) the widest.

Choice (4) is the correct answer.

12. At Berkeley Central High School, a survey was conducted to see if students preferred cheeseburgers, pizza, or hot dogs for lunch. The results of this survey are shown in the table below.

Based on this survey, what percent of the students preferred pizza?

1) 30
2) 37
3) 44
4) 74

Since the want to know the percent of all students, you need to find how many (males and females) are in the survey and the total that prefer Pizza.

There are 44 + 30 = 74 who prefer pizza.

There are 32 + 36 + 44 + 30 + 24 + 34 = 200 students.

74/200 = 37%, which is Choice (2).

Choice (1) is the number of Males, and not a percent.

Choice (3) is the number of Females, and not a percent.

Choice (4) is the total number, but not a percent.

13. Which situation could be modeled by a linear function?

1) The value of a car depreciates by 7% annually
2) A gym charges a \$50 initial fee and then \$30 monthly
3) The number of bacteria in a lab doubles weekly.
4) The amount of money in a bank account increases by 0.1% monthly.

Answer: 2) A gym charges a \$50 initial fee and then \$30 monthly

In Choice (2), there is an initial value and a constant monthly rate. This is the same as a y-intercept and a constant slope. Choice (2) is the correct answer.

Choice (1) shows exponential decay because 7% of one year will be smaller than 7% of the year before. It is not a constant change.

Choice (2) shows exponential growth because double last week is not the same increase as doubling the week before that.

Choice (4) shows exponential growth even if it is very slow growth.

14. Which function has the smallest y-intercept value?

The y-intercept value occurs when x = 0 (at the y-axis).

In Choice (1), the y-intercept is 1.

In Choice (2), the y-intercept is -3, so eliminate Choice (1).

In Choice (3), the y-intercept is -2. Eliminate Choice (3).

In Choice (4), the y-intercept is -1. Eliminate Choice (4).

Choice (2) is the correct answer because h(0) = -3.

15.When solving x2 - 10x - 13 = 0 by completing the square, which equation is a step in the process?

1) (x - 5)2 = 38
2) (x - 5)2 = 12
3) (x - 10)2 = 38
4) (x - 10)2 = 12

Answer: 1) (x - 5)2 = 38

When you complete the square, the value of b (the coefficient in front of the x term) is halved. So Eliminate Choices (3) and (4).

Half of 10 is 5, and 5 sqaured is 25.

x2 - 10x + 25 - 13 = 25

x2 - 10x + 25 = 38

(x - 5)2 = 38

More to come. Comments and questions welcome.

More Regents problems.

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