The equation of the curve is: \(y=x^2-5x+4\)
This is a quadratic equation in standard form, where the coefficient of the \(x^2\) term is 1, the coefficient of the \(x\) term is -5, and the constant term is 4.
The graph of a quadratic equation is a parabola. The coefficient of the \(x^2\) term determines whether the parabola opens upwards or downwards. In this case, since the coefficient is positive, the parabola opens upwards.
To find the vertex of the parabola, we can use the formula: \(-\frac{b}{2a}\), where \(a\) is the coefficient of the \(x^2\) term and \(b\) is the coefficient of the \(x\) term. Substituting the values, we get:
\(-\frac{b}{2a}=-\frac{-5}{2(1)}=\frac{5}{2}\)
So the vertex is at \(\left(\frac{5}{2},\frac{1}{4}\right)\).
Therefore, the equation of the curve is \(y=x^2-5x+4\).
