Mixed Function Intersection Analysis using GDC Technology

00:00 7 marks

Using a computer-based Graph Display Calculator (GDC), analyze the intersection between the linear function \(f(x)=2x+1\) and the quadratic function \(g(x)=-x^2+6\). Answer the following parts:

Part a

3 minutes 2 marks

Question

Define the functions \(f(x)=2x+1\) and \(g(x)=-x^2+6\) on your GDC. Describe their key characteristics including domain, range, and general behaviour.

Hint Hint

Hint

Focus on identifying the type of each function and note how a linear function differs from a quadratic one.

Answer Answer
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Complete Answer

f(x)=2x+1 is a linear function with a constant slope of 2 and a y-intercept of 1. g(x)=-x^2+6 is a quadratic function opening downwards with a vertex at (0,6). The domain for both functions is all real numbers; the range of g(x) is limited by its maximum value at the vertex.

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Part b

4 minutes 2 marks

Question

Using your GDC, determine the approximate intersection point(s) of \(f(x)\) and \(g(x)\) by locating where their graphs cross.

Hint Hint

Hint

Utilize the intersection tool available on your GDC.

Answer Answer
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Complete Answer

The GDC indicates two approximate intersection points: one at \(x \approx 1.45\) with \(y \approx 3.90\), and another at \(x \approx -3.45\) with \(y \approx -5.90\).

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Part c

3 minutes 3 marks

Question

For HL, provide the refined intersection coordinates with each value rounded to three decimal places.

Hint Hint

Hint

Use the numeric refinement function on your GDC or solve analytically and round to three decimal places.

Answer Answer
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Answer Answer

Complete Answer

Intersection points refined: \((1.449, 3.898)\) and \((-3.449, -5.898)\).

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