Question

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

Answer 1

Draw the graph of `2x^2-3x+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 `2x^2-3x+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 `(-b)/(2a)` = `3/4`. Plugging this back in gives `y = 2.875`.

Since the quadratic is positive, and `(3/4, 2.875)` is the lowest point, the line doesn't intercept the `x` axis at any point. Hence, there are no solutions.