Mathematics 10 — Exercise 2.1 · Q5 (i)

Full question

Solve the following quadratic equation graphically: x²-3 × x-18 = 0.

x^{2} - 3 \times x - 18 = 0

Step-by-step solution

Draw y equal to the quadratic. Its x-axis intersections occur where y = 0.
$y = x^{2} - 3 \times x - 18$
Locate the vertex: x = −b/(2a), then put this x back into the function for y.
$(\frac{3}{2}, - \frac{81}{4})$
Calculate the table points, plot them and join with a smooth parabola.
Read the x-coordinates of the points where the curve meets the x-axis.
${-3, 6}$

x	y
-4	10
-3	0
-2	-8
-1	-14
0	-18
1	-20
2	-20
3	-18
4	-14
5	-8
6	0
7	10

Answer

The final answer is shown below.

{-3, 6}