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Back to Tutor Intake Assessment: Explain intersection as solution

HSA.REI.D.11 Tutor Intake -- Intersections as Solutions

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question without help. If you are not sure, give your best try — the goal
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Grade 9·6 problems·~11 min·Common Core Math - HS Algebra·standard·hsa-rei-d-11
Work through problems with immediate feedback
A

Concepts

1

The graphs of y=f(x)y = f(x) and y=g(x)y = g(x) intersect at the point (3,5)(3, 5).

What does this tell us about the equation f(x)=g(x)f(x) = g(x)?

2

A student uses graphing technology and reads an intersection point as
approximately x=2.3x = 2.3.

The student says: "The exact solution to the equation is x=2.3x = 2.3."

Is the student correct?

3

To solve 3x−2=x2−43x - 2 = x^2 - 4 graphically, a student graphs only y=x2−4y = x^2 - 4.

What error did the student make?

B

Procedures

1

A graph shows that y=x+1y = x + 1 and y=x2−1y = x^2 - 1 intersect at
two points: approximately (−1,0)(-1, 0) and (2,3)(2, 3).

What are the approximate solutions to x+1=x2−1x + 1 = x^2 - 1?

2

How many solutions does ∣x−1∣=x2−3|x - 1| = x^2 - 3 have, based on the
description that the graphs of y=∣x−1∣y = |x - 1| and y=x2−3y = x^2 - 3
intersect at three points?

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