HELP_ME123 said:one of my homework questions is asking to find the equation in standard form when given the roots and one intersecting point. The roots are -2 and 8 and
point given is -1,16. any help much appreciated.
courtrigrad said:Is this a quadratic? [tex] f(x) = a(x - h)^2 + k [/tex]
A quadratic equation is a mathematical expression that contains a variable raised to the second power, also known as a squared term. It can be written in the form ax2 + bx + c = 0, where a, b, and c are constants and x is the variable.
The roots of a quadratic equation can be found by using the quadratic formula: x = (-b ± √(b2 - 4ac)) / 2a. This formula gives the two possible values for x when the quadratic equation is equal to 0. These values are also known as the solutions or zeros of the equation.
Solving a quadratic equation given roots and a point means finding the specific quadratic equation that has the given roots and also passes through the given point. This involves using the roots to determine the values of a, b, and c in the standard form of a quadratic equation, ax2 + bx + c = 0, and then substituting the coordinates of the given point into the equation to solve for the remaining unknown variable.
No, a quadratic equation can only have a maximum of two distinct roots. This is because the graph of a quadratic function is a parabola, which can only intersect the x-axis in two points at most.
To check if a given point is a solution to a quadratic equation, substitute the coordinates of the point into the equation and see if the resulting statement is true. If the statement is true, then the point is a solution to the equation. If the statement is false, then the point is not a solution to the equation.