How do you graph the inequality #y<2x^2+3x-5#?

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Answer 1 · 2018-05-03T07:42:02

#" "#
Please read the explanation.

#" "#
Given the inequality: #color(blue)(y<2^2+3x-5#

#color(green)("Step 1:"#

Make a table of values: #color(red)(x# and corresponding values for #color(red)(y#

enter image source here

#color(green)("Step 2:"#

Replace the inequality sign with #color(red)(=# sign and graph the quadratic equation.

Use dashed lines for this graph as the inequality sign is: #color(red)(<#

Construct the graph:

enter image source here

Obviously, all the points in table will lie on the graph as shown in the graph.

#color(green)("Step 3:"#

In this step, choose a few test points or coordinates NOT on the parabola.

This is the required region that satisfies our original inequality.

Shade the region as shown:

enter image source here

Hope it helps.