# How do you solve the equation by graphing 2x^2 - 3x + 4 = 0?

Dec 15, 2017

Draw the graph of $2 {x}^{2} - 3 x + 4$ and see where it intercepts the $x$ axis to solve for $x$. In this case, there are no solutions.

#### Explanation:

We can sketch the graph of $2 {x}^{2} - 3 x + 4$ using the following facts:

• The $y$ intercept is $4$
• The $b$ term ($- 3$) is negative, so the graph is shifted slightly to the right
• The x coordinate of the vertex is $\frac{- b}{2 a}$ = $\frac{3}{4}$. Plugging this back in gives $y = 2.875$.

Since the quadratic is positive, and $\left(\frac{3}{4} , 2.875\right)$ is the lowest point, the line doesn't intercept the $x$ axis at any point. Hence, there are no solutions.