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Research by Cipriano et al. (2023) indicates that social-emotional learning (SEL) instruction increases _____, and decreases _____.

Which of the following graphs shows the solution to ?

Interpret the Solution(s) on the Graph: How would the solution(s) appear on the graph of ?

Continue Solving: After both sides of the equation are squared, the next step is to collect all terms on one side of the equation. Which of the following is the equation that results when all terms have been collected on one side?

Interpret the Solution(s) Graphically: The graph below was generated by sketching functions from the radical equation . The blue curve is the function  and represents the left side of the equation. The red curve is the function  and represents the right side of the equation. The dotted gold curve is the function . This represents the bottom half of the parabola that is NOT part of the equation. Click on the part of the graph that shows the actual solution to the radical equation .

Solve the Quadratic Equation: Since the function on the left side is a 2nd degree trinomial, the equation can be solved by either or . The solution(s) to this quadratic equation are (smaller value) and (larger value). The solutions to the quadratic equation are potential solutions to the square root equation.

Summarize how solution(s) to equations are interpreted graphically.   In any equation, each side of the equation can be represented as an individual . When the two are graphed on the same coordinate axes, the solution(s) are located where the two graphs . The -value(s) of these points is/are the solution(s) to the equation.   When one side of the equation is , the second function is the line y = 0 that is also the . In this situation, the are located directly on the .

Continue Solving: Once we have taken action to bring the  out of the exponent, what is the resulting equation?

Find the Solution(s): Now that the equation is factored, set each factor equal to zero and solve for . What is/are the solution(s)?   Note: If there is only one solution, enter it in both blanks below. If there is No Solution, simply type the letter N in both blanks.   The smaller of the two solutions is x = {}.  The larger of the two solutions is x = {}.

Set up the Equations: Absolute value represents distance. Absolute value equations separate into two separate equations because we must consider the distance in both the left and right directions.   The equation splits into these two equations: Equation in the left direction:   Equation in the right direction: