Mathematics 10 — Exercise 2.1 · Q5 (ii)

Full question

Solve the following quadratic equation graphically: x²-5 × x-14 = 0.

x^{2} - 5 \times x - 14 = 0

Step-by-step solution

Draw y equal to the quadratic. Its x-axis intersections occur where y = 0.
$y = x^{2} - 5 \times x - 14$
Locate the vertex: x = −b/(2a), then put this x back into the function for y.
$(\frac{5}{2}, - \frac{81}{4})$
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.
${-2, 7}$

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

Answer

The final answer is shown below.

{-2, 7}