Graphing Lab

SAT Math Mastery with Desmos

Student:

Date:

Instructions: Use the Desmos Graphing Calculator to solve the following SAT-style questions. Focus on using graphing to find intersections, analyzing function transformations, and performing complex statistical or algebraic computations. Show any key coordinates or equations you used in the "Work Area".

1

The graphs of the equations \( y = x^2 - 5x + 4 \) and \( y = 2x - 6 \) intersect at two points in the xy-plane. What is the product of the x-coordinates of these two intersection points?

Desmos Work Area: Graph both equations

Product of x-coordinates:

2

The function \( f \) is defined by \( f(x) = -2(x - 3)^2 + 8 \). Which of the following is an x-intercept of the graph of \( y = f(x) \) in the xy-plane?

A) 1

B) 3

C) 5

D) 8

Desmos Strategy: Root finding

3

A list of data values consists of the following numbers: \( \{12, 15, 15, 17, 22, 28, 30, 45, 102\} \). What is the difference between the mean and the median of this data set? (Round to the nearest tenth).

Work Area: Use Desmos list L = [...]

Result:

4

Which of the following points \( (x, y) \) is a solution to the system of inequalities shown below? y > 2x + 1
y < -0.5x + 5

A) (0, 0)

B) (1, 4)

C) (3, 2)

D) (-2, 6)

Desmos Hint: Graph and check point labels

5

Let \( g(x) = x^3 - 4x \). If the graph of \( h \) is the result of shifting the graph of \( g \) right by 3 units and up by 2 units, what is the value of \( h(2) \)?

Work Area: Write h(x) in terms of g(x) in Desmos

h(2) =

6

A gallery records the following number of visitors over 7 days: \( \{12, 18, 24, 30, 36, 42, 48\} \). If a busy day with 100 visitors is added to the data, what is the positive difference between the median of the original data and the median of the new data?

Work Area: Use median(L) and median(M) in Desmos

Difference:

7

Consider the function \( p(x) = \frac{x^2 - 16}{x - 4} \). What is the y-coordinate of the hole in the graph of \( p \)?

Desmos Method: Zoom in or use tables

y-coordinate:

8

How many distinct solutions are there for the equation \( |2x - 5| = x + 1 \)?

Graph both sides separately in Desmos

Number of Solutions:

9

A circle in the xy-plane has the equation \( x^2 + y^2 - 6x + 8y = 0 \). What is the radius of this circle?

Graph the circle and find the center/edge

Radius:

10

The graphs of \( y = x^3 - 3x^2 + 2 \) and \( y = x - 1 \) intersect at three points. What is the sum of the x-coordinates of these three intersection points?

Show Intersection points here

Sum:

Desmos Power Up

Graphing Lab Worksheet

Graphing Lab Answer Key

Desmos Pro Slides

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