Question

Find the x-intercepts of the graph of the equation. $$y=2 x^{2}-6 x-8$$

Short answer

The x-intercepts of the graph of the equation are \(x = 4\) and \(x = -1\)

Step-by-step solution

Write Down the Quadratic Equation

The given quadratic equation is \(y = 2x^{2} - 6x - 8\).

Set y to 0 and Make the Equation Standard

We are looking for the points where the equation crosses the x-axis. For this, we set y = 0, because the y-value at the x-axis is 0. We can write down the following equation: \(0 = 2x^{2} - 6x - 8\)

Find the x-Intercepts by Solving Quadratic Equation

We solve the equation \(0 = 2x^{2} - 6x - 8\) for \(x\). First, divide the equation by two to simplify it, which gives \(0 = x^{2} - 3x - 4\). Then we factorize which gives \((x-4)(x+1) = 0\). Setting each factor to zero gives the solutions \(x = 4\) and \(x = -1\)