The diagram below shows the graph of y=2x^2-5x-2 and the lines y=-2x+3 and y=2x-2 By first identifying the appropriate line, use the diagram to estimate the solutions to 2x^2-5x-2=-2x+3 graphically. Give any decimal answers to 1 decimal place.

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The diagram below shows the graph of y=2x^2-5x-2 and the lines y=-2x+3 and y=2x-2 By first identifying the appropriate line, use the diagram to estimate the solutions to 2x^2-5x-2=-2x+3 graphically. Give any decimal answers to 1 decimal place.

Answer 1

The graphical solutions to \(2x^2-3x-5 = 0\) are approximately \(x ≈ 1.5\) and \(x ≈ 1.9\).

Answer 2

## Step 1: To solve the equation graphically, we first set the quadratic and linear equations equal to each other. This gives us \(2x^2-5x-2 = -2x+3\). ## Step 2: Compose the equations to a simplified one by eliminating the like terms from both sides of our expression. We find that after combining, our equation is simplified to \(2x^2-3x-5 = 0\). ## Step 3: To visualize this equation graphically, we will assume our simplified quadratic equation equals to \(y\). This converts the equation into \(y = 2x^2-3x-5\). ## Step 4: Then, we need to find where this new graph for the quadratic expression intersects with the line graph if \(y = -2x + 3\). Because the intersections of these two graphs will represent the solutions to our equation. ## Step 5: By observing the graph, we find that the curve \(y = 2x^2-3x-5\) intersects the line \(y = -2x + 3\) at about two places. Ideally, we need to place them closer to the exact integer values, however, in this question they are meant to be stated in their decimal places, hence the approximation. Do these steps accurately for high precision solutions.

Question

The diagram below shows the graph of y=2x^2-5x-2 and the lines y=-2x+3 and y=2x-2 By first identifying the appropriate line, use the diagram to estimate the solutions to 2x^2-5x-2=-2x+3 graphically. Give any decimal answers to 1 decimal place.

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