Question Type 1: Constructing simple graphs to solve equations Exercises

By sketching the graphs of $y = x^2$ and $y = 5x - 4$, find the solutions to $x^2 = 5x - 4$.

Sketch the graphs of $y = x^2$ and $y = x + 2$, then solve $x^2 = x + 2$.

Solve graphically the equation $x^2 = 4 - x$ by sketching the graphs of $y = x^2$ and $y = 4 - x$, and estimate the solutions. Verify your results algebraically.

By plotting $y = x^2$ and $y = 3x + 2$, find graphically the solutions of $x^2 = 3x + 2$.

Sketch the graphs of $y = x^2$ and $y = -x + 4$, then solve $x^2 = -x + 4$.

Sketch the graphs of $y = x^2$ and $y = 2x + 3$, and hence find the exact solutions to the equation $x^2 = 2x + 3$.

By plotting $y = x^2$ and $y = 2 - 0.5x$, find the approximate solutions to $x^2 = 2 - 0.5x$.

Solve graphically the equation $x^2 = -3x + 5$ by plotting $y = x^2$ and $y = -3x + 5$, and give approximate solutions.

Sketch $y = x^2$ and $y = 3$, then determine graphically the solutions to $x^2 = 3$.

Sketch the graphs of $y = x^2$ and $y = 2x + 1$, and hence solve $x^2 = 2x + 1$.

Solve graphically the equation $x^2 = 6 - x$ by sketching the graphs of $y = x^2$ and $y = 6 - x$, and state the values of $x$.

Solve graphically $x^2 = -x + 2$ by drawing $y = x^2$ and $y = -x + 2$, and state the solutions.