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

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Answer 1 · 2018-05-03T07:42:02

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Please read the explanation.

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**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 ** $color(red)(y$

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

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.

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