This is the concept of quadratic equations. The equation has the original form of y=ax^2+bx+c. Our equation is given by y=x^2-6x+9. Since our leading coefficient is positive, then it means that our function will not be negative at any point. In other words, the range is [0,∞). Hence we conclude that the function will be no where negative.
A real numbers are numbers that can be found on a number line, they include both rational and irrational numbers. We can first solve the equation; x² - 6x + 9 =0, using completing square method; x²- 6x + (-3)² = -9 + (-3)² (x-3)² = 0 x = 3 therefore, both values of x are 3, thus the expression has no real number x is negative.
