Professional Analysis of Quadratic Function
What is the leading coefficient of the quadratic function represented by f(x)=8x²-7x+6?
Choose one:
a) 8
b) -7
c) 6
Answer:
The leading coefficient of the quadratic function represented by f(x)=8x²-7x+6 is 8.
When dealing with quadratic functions in the form f(x)=ax²+bx+c, the leading coefficient is the coefficient of the x² term, which in this case is 8. This coefficient determines the shape and direction of the parabola that represents the quadratic function.
In the given function f(x)=8x²-7x+6, the leading coefficient is 8, which means the parabola opens upwards.
The leading coefficient plays a crucial role in determining whether the quadratic function has a minimum or maximum value and in analyzing the behavior of the function as x approaches positive or negative infinity.