Algebra Problems of the Day (Algebra Regents, June 2025 Part III)

This exam was adminstered in June 2025.

June 2025 Algebra, Part III

Each correct answer is worth up to 4 credits. Partial credit can be given. Work must be shown or explained.

31. Graph f(x) = -3x and g(x) = x² + 2 on the set of axes below.

State the values of x that satisfy the equation f(x) = g(x)

Answer:

Use your graphing calculator to find the points that you need to point. Determine for which x values that the graphs intersect. Only answer the x values, do not give coordinates in your answer.

The equation f(x) = g(x) is true when x = -1 or x = -2.

This could've been solved algebraically for partial credit.

32. Using the quadratic formula, solve 6x² + 2x - 1 = 0.
Express the answer in simplest radical form.

Answer:

Use the quadratic formula with a = 6, b = 2, and c = -1.

( -(2) + √( (2)² - 4(6)(-1) ) ) / ( 2(6))
( -2 + √( 4 - (-24) ) ) / 12
( -2 + √(28) ) / 12
( -2 + √( (4)(7) ) ) / 12
( -2 + 2√(7) ) / 12
( -1 + √(7) ) / 6

33. The table below shows the price of a new cell phone and the length of time, in months, since its release.

State the linear regression equation for this set of data. Round all values to the nearest hundredth.

State the correlation coefficient for this data set, to the nearest hundredth.

State what the correlation coefficient indicates about the linear fit of the data.

Answer:

Put the data into Lists L₁ and L₂. Make sure that "DiagnosticOn" has been executed. (It's in the Catalogue.) Run a Linear Regression.

The equation for the linear equation will be y = -23.67x + 1216

The correlation coefficient is r = -0.99.

The correlation coefficient indicates a strong correlation.

There isn't much to say about this. Either you know how to enter the data and run the linear regression, or you do not.

Or you copy the answers from the people next to you, which may or may not get you into trouble.

34. Solve the following system of equations algebraically for all values of x and y.

y = x² + 9x + 4
y - 2x = -6

Answer:

Isolate the y in the second equation. Then set the two expressions equal to each other and then solve the quadratic equation. After that, find the value of y that corresponds to each value of x.

x² + 9x + 4 = 2x - 6
x² + 7x + 10 = 0
(x + 5)(x + 2) = 0
x + 5 = 0 or x + 2 = 0
x = -5 or x = -2

If x = -5: y = 2(-5) - 6 = -16
If x = -2: y = 2(-2) - 6 = -10.

End of Part III

How did you do?

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