Question

How do you solve ${x^2} - x - 12 = 0$ graphically?

Answer 1

Hint: To solve a quadratic equation by graph, we put $y = {x^2} - x - 12$.
For different values of $x$, we can find different values of $y$ .
Substitute $x = 0,3, - 4$ into the equation $y = {x^2} - x - 12$ we get $y$- values accordingly.
For each value of x and y we get the coordinate (x,y).
Draw the graph by drawing each coordinate. The point where the graph of $y = {x^2} - x - 12$ cuts x-axis those x values are the solution of the equation.

Complete step-by-step solution:
The quadratic equation is given as: ${x^2} - x - 12 = 0$.
Assume that the function is defined as $y = {x^2} - x - 12$.
Substitute $x = 0$ into the equation $y = {x^2} - x - 12$,
$\Rightarrow$$y = {0^2} - 0 - 12$
$\Rightarrow$$y = - 12$
The point is $(0, - 12)$ .
Substitute $x = 4$ into the equation $y = {x^2} - x - 12$,
$\Rightarrow$$y = {(4)^2} - 4 - 12$
$\Rightarrow$$y = 16 - 4 - 12$
$\Rightarrow$$y = 0$
The point is $(4,0)$ .
Substitute $x = - 3$ into the equation $y = {x^2} - x - 12$,
$\Rightarrow$$y = {( - 3)^2} - ( - 3) - 12$
$\Rightarrow$$y = 9 + 3 - 12$
$\Rightarrow$$y = 0$
The point is $( - 3,0)$ .
The coordinates are $(0, - 12)$,$(4,0)$ and $( - 3,0)$ . Draw the graph of the equation $y = {x^2} - x - 12$.

From the graph the solution of the ${x^2} - x - 12 = 0$ is the x-values where the y-values become zero.

Note: Solve the equation by the analytical method,
Find the factors of the equation,
${x^2} - x - 12 = 0$
$ \Rightarrow (x - 4)(x + 3) = 0$
When,
$x - 4 = 0$
$ \Rightarrow x = 4$
When,
$x + 3 = 0$
$ \Rightarrow x = - 3$
The solution of the equation ${x^2} - x - 12 = 0$ is $x = 4$ or $x = - 3$