We are asked to solve the given quadratic equation. We will solve it by graphing. To solve a quadratic equation by graphing, we have to follow three steps.
The solutions, or roots, of ax^2+bx+c=0 are the x-intercepts of the graph of f(x)=ax^2+bx+c.
Now we can identify the function related to the equation.
Equation:& 2x^2-8x=0
Related Function:& f(x)=2x^2-8x
Graphing the Related Function
To draw the graph of the related function written in standard form, we must start by identifying the values of a, b, and c.
f(x)=2x^2-8x
⇕
f(x)= 2x^2+( - 8)x+ 0
We can see that a= 2, b= - 8, and c= 0. Now, we will follow three steps to graph the function.
We can finally draw the graph of the function. Since a= 2, which is positive, the parabola will open upwards. Let's connect the points with a smooth curve.
Finding the x-intercepts
Let's identify the x-intercepts of the graph of the related function.
We can see that the parabola intersects the x-axis twice. The points of intersection are ( 0,0) and ( 4,0). Therefore, the equation 2x^2-8x=0 has two solutions, x= 0 and x= 4.
