The solutions, or roots, of ax^2+bx+c=0 are the x-intercepts of the graph of f(x)=ax^2+bx+c. Let's write our equation in standard form. This means gathering all of the terms on the left-hand side of the equation.
2x^2 = -24x - 72
⇕
2x^2 + 24x + 72 = 0
Now we can identify the function related to the equation.
To draw the graph of the related quadratic function written in standard form, we must start by identifying the values of a, b, and c.
f(x)= 2x^2+24x+72=0
⇕
f(x)= 2x^2+ 24x+ 72
We can see that a= 2, b= 24, and c= 72. 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 only once. The point of intersection is ( - 6,0). Therefore, the equation x^2+24x+72=0 has one solution, - 6.
