Objective:
Train students to skip the manual algebra entirely. Open Desmos Graphing Calculator in a split screen and solve these by identifying intersection points, table values, or shifts.
Questions 1. If 3x - 2y = 12 and x + 4y = 18, what is the value of y? 2. A quadratic function is defined by f(x) = -2(x - 3)² + 8. What is the maximum value of f(x)? 3. Find the y-coordinate of the intersection for the system:\(y=x^{2}-4x+5\)\(y=2x-3\) 4. If g(x) = 3x - 7 and g(k) = 14, what is the value of k? 5. How many solutions does the system y = 3x + 5 and 2y - 6x = 10 have? 6. What is the x-intercept of the line 4x - 7y = 28? 7. For what value of b will the equation x² + bx + 16 = 0 have exactly one real solution? 8. If \(f(x) = 2^x + 3\), what is the value of f(4)? 9. Find the intersection of 1.3x - 0.6y = -0.7 and 6.5x - 1.5y = -0.5. What is the y-coordinate? 10. The graph of y = x² is shifted 3 units left and 5 units up. Write the resulting equation.
🔑 Answer Key & Desmos Guide 1. 3 → Type both lines into Desmos. Look at the intersection point (6, 3). The y-value is 3. 2. 8 → Type the function. Look at the vertex peak at (3, 8). The maximum value is the y-coordinate. 3. 1 → Type both curves. They touch at (4, 5) and (2, 1). The question asks for the y-coordinate of an intersection; 1 or 5 are correct. 4. 7 → Type y = 3x - 7 and y = 14. Find where they cross at x = 7. 5. Infinitely many → Type both. They overlap perfectly as the same line. 6. 7 → Type the equation. Click the spot where it crosses the horizontal x-axis: (7, 0). 7. 8 or -8 → Type y = x² + bx + 16. Add a slider for b. Move the slider until the bottom of the parabola sits exactly on the x-axis. 8. 19 → Type \(f(x) = 2^x + 3\). On the next line, type f(4) to instantly see the output. 9. 2 → Type both decimal equations into Desmos. Zoom in slightly to locate the intersection point (0.5, 2). 10. y = (x + 3)² + 5 → Type y = x² first. Type the answer options to see which one accurately moves left and up.📐