EOC Systems Linear/Quad & Transformations Quad/Exponential

The graph of f(x) and g(x) are shown below. How many solutions does the system of equations have?

• One

• Two

• Three

• Four

• No Solution

Answer explanation

The graphs of f(x) and g(x) intersect at three distinct points, indicating that the system of equations has three solutions. Therefore, the correct answer is 'Three'.

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Tags

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.12

What are the solutions to the system of equations graphed below?

• (2, 0)

• (0, 4)

• (-2,0)

• (0, -4)

• No Solution

Answer explanation

The solutions to the system of equations are the points where the lines intersect. The points (2, 0) and (-2, 0) are where the lines meet, confirming they are the correct solutions.

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• I reviewed the correct answer and I understand my mistake(s)

• I did not review the correct answer

• I reviewed the correct answer and I DO NOT understand my mistake(s)

• I got the last question correct

If a nonlinear system contains a linear function that never touches the quadratic function, that system has...

• 2 solutions

• 1 solution

• No solutions

• Infinite solutions

Answer explanation

Since the linear function never touches/crosses/meets the quadratic function, there are no points of intersection. Therefore, the system has no solutions.

Determine the number of solutions to the given linear-quadratic system.

• 0 solutions

• 1 solution

• 2 solutions

• 3 solutions

Answer explanation

The system consists of a linear equation and a quadratic equation. The quadratic can intersect the linear at two points, leading to 2 solutions. Thus, the correct answer is 2 solutions.

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• I reviewed the correct answer and I understand my mistake(s)

• I did not review the correct answer

• I reviewed the correct answer and I DO NOT understand my mistake(s)

• I got the last question correct

Determine the solution to the given linear-quadratic function.

• (0, 0)

• (3, 0)

• (2, -3)

• (0, -3)

Answer explanation

The solution to the linear-quadratic function is found by substituting values. (2, -3) satisfies the equation, making it the correct choice. The other options do not fulfill the function's requirements.

Use the image to check for the correct work/explanation. Then select a choice below.

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• I did not review the correct answer

• I reviewed the correct answer and I DO NOT understand my mistake(s)

• I got the last question correct

Two equations were graphed on the set of axes below.  Which point is a solution to the system of equations ?

• (0,3)

• (5,0)

• (2,-3)

• (8,9)

Answer explanation

The point (8,9) is a solution to the system of equations because it lies at the intersection of the two graphed lines, satisfying both equations. The other points do not meet this criterion.