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

1 Answer
Dec 15, 2017

Answer:

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#.

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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.