Mathematics 10 — Exercise 2.1 · Q5 (iv)

Full question

Solve the following quadratic equation graphically: 4 × x²+12 × x-27 = 0.

Step-by-step solution

1. Draw y equal to the quadratic. Its x-axis intersections occur where y = 0.

   $$y=4\times x^2+12\times x-27$$

2. Locate the vertex: x = −b/(2a), then put this x back into the function for y.

   $$(-\frac{3}{2},-36)$$

3. Calculate the table points, plot them and join with a smooth parabola.

4. Read the x-coordinates of the points where the curve meets the x-axis.

   $$\{-\frac{9}{2},\frac{3}{2}\}$$

Answer

The final answer is shown below.