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. Let's write our equation in standard form. This means gathering all of the terms on the left-hand side of the equation.
- 9 = x^2 ⇔ x^2+9=0
Now we can identify the function related to the equation.
Equation:& x^2+9=0
Related Function:& f(x)=x^2+9
Graphing the Related Function
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)=x^2+9
⇕
f(x)= 1x^2+ 0x+ 9
We can see that a= 1, b= 0, and c= 9. Now, we will follow three steps to graph the function.
We can finally draw the graph of the function. Since a=1, which is positive, the parabola will open upwards. Let's connect the points with a smooth curve.
We can see that the parabola does not intersect the x-axis. Therefore, it has no real solutions.
