Table of Contents
What are the roots of this quadratic function?
The roots of a function are the x-intercepts. By definition, the y-coordinate of points lying on the x-axis is zero. Therefore, to find the roots of a quadratic function, we set f (x) = 0, and solve the equation, ax2 + bx + c = 0.
What is √ B² 4ac 2a?
The quadratic formula is x=(-b±√(b²-4ac))/(2a). The discriminant is the part under the radical, b²-4ac. The discriminant denotes the number of real solutions.
What is b2 4ac?
The quantity b2−4ac is called the discriminant of the polynomial. If b2−4ac < 0 the equation has no real number solutions, but it does have complex solutions. If b2−4ac = 0 the equation has a repeated real number root. If b2−4ac > 0 the equation has two distinct real number roots.
How do you find a quadratic function with no real roots?
An example of a quadratic function with no real roots is given by, f ( x) = x2 − 3 x + 4. b2 −4 ac = (−3) 2 − 4 · 1 · 4 = 9 − 16 = −7.
How do you find the nature of the solutions of quadratic functions?
This is used to determine the nature of the solutions of a quadratic function. Example 1: Determine the vertex of the quadratic function f (x) = 2 (x+3) 2 – 2. Example 2: Solve the quadratic function f (x) = x 2 + 3x – 4 using the quadratic functions formula. Solution: The quadratic function f (x) = x 2 + 3x – 4.
What is an example of a quadratic equation?
Example 1: Determine the vertex of the quadratic function f (x) = 2 (x+3) 2 – 2. Example 2: Solve the quadratic function f (x) = x 2 + 3x – 4 using the quadratic functions formula. Solution: The quadratic function f (x) = x 2 + 3x – 4.
What is the discriminant of a quadratic function with two real roots?
If the discriminant of a quadratic function is greater than zero, that function has two real roots ( x -intercepts). Taking the square root of a positive real number is well defined, and the two roots are given by, f ( x) = 2 x2 − 11 x + 5. b2 − 4 ac = (−11) 2 − 4 · 2 · 5 = 121 − 40 = 81.