Question

How do you solve the equation `4x^2-7x-15=0` by graphing?

Answer 1

`x = -1.25, 3`

Explanation:

Given: `y = 4x^2 - 7x - 15 = 0`

Solve means find the `x` values that make `y = 0`. These values are called `color(blue)("zeros")` or `x`-intercepts when given as a point.

Graph the function: `4x^2 - 7x - 15`

graph{4x^2 - 7x - 15 [-10, 10, -20, 10]}

On a TI 83, 83+, 84, 84+, to find the first zero , you would use:

2nd Calc 2 . zero ENTER

The calculator asks: Left Bound?

You move the cursor using the arrow keys until you are to the left and above the `x`-axis (`y = 0`) near where the parabola crosses the `x`-axis.. Then press ENTER

The calculator asks: Right Bound?

You move the cursor using the arrow keys until you are to the right and below the `x`-axis (`y = 0`). Then press ENTER

The calculator asks: Guess?

You can just press ENTER unless there are two zeros really close to each other. Then you would need to move the cursor closer to the one you want.

Calculator says: Zero X = -1.25 Y = 0

To find the 2nd zero:

2nd Calc 2 . zero ENTER

You move the cursor using the arrow keys until you are to the left and below the `x`-axis (`y = 0`) near where the parabola crosses the `x`-axis. Then press ENTER

The calculator asks: Right Bound?

You move the cursor using the arrow keys until you are to the right and above the `x`-axis (`y = 0`) near where the parabola crosses the `x`-axis. Then press ENTER

The calculator asks: Guess?

You can just press ENTER unless there are two zeros really close to each other. Then you would need to move the cursor closer to the one you want.

Calculator says: Zero X = 3 Y = 0