The solutions, or roots, of ax^2+bx+c=0 are the x-intercepts of the graph of f(x)=ax^2+bx+c. Note that our equation is already in standard form. We will identify the function related to the equation.
Equation:& x^2 - 16x + 64 = 0
Related Function:& f(x)= x^2 - 16x + 64
Graphing the Related Function
To draw the graph of the given quadratic function written in standard form, we must start by identifying the values of a, b, and c.
y=x^2-16x+64
⇕
y= 1x^2+( -16)x+ 64
We can see that a= 1, b= -16, and c= 64. 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.
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 once. The point of intersection is ( 8,0). Therefore, the equation x^2-16x+64=0 has one solution, x=8.
