# How do you solve x^2 + 3x - 4 = 0 graphically and algebraically?

Jul 22, 2016

#### Answer:

$x = 1$
$x = - 4$

#### Explanation:

Given -

${x}^{2} + 3 x - 4 = 0$

Algebraic Solution

${x}^{2} - x + 4 x - 4 = 0$
$x \left(x - 1\right) + 4 \left(x - 1\right) = 0$
$\left(x - 1\right) \left(x + 4\right) = 0$
$x = 1$
$x = - 4$

If you take the above equation as a function as

$y = {x}^{2} + 3 x - 4$

One Solution is

$\left(1 , 0\right)$

Another solution is

$\left(- 4 , 0\right)$

To have a graphic solution, You have identify a range of

values for $x$ That includes vertex and the above said two points.

Its vertex is given by -

$x = \frac{- b}{2 \times a} = \frac{- 3}{2 \times 1} = - \frac{3}{2}$

Now take four values above and below $- \frac{3}{2}$

Find the corresponding $y$ values for $x$

Plot all the values. Those co-ordinates where the curve cuts the x-axis is the graphic solution to the problem.