Solve Quadratic Equation Given Roots & Point

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In summary, the conversation is about finding the equation in standard form when given two roots and one intersecting point. The roots are -2 and 8, and the point given is -1, 16. The equation must be of the form f(x) = a(x-8)(x+2) to have those roots. The value of a needs to be determined in order for f(-1) to equal 16. It is mentioned that the equation could also be a function, where for every x value there is only one y value. It is suggested that the original response may have been asking if the person knows what a quadratic is.
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HELP_ME123
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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.
 
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  • #2
Is this a quadratic? [tex] f(x) = a(x - h)^2 + k [/tex]
 
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  • #3
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.

So you know it must be of the form f(x)= a(x-8)(x+2) in order to have those roots. What must a be so that f(-1)= 16?
 
  • #4
courtrigrad said:
Is this a quadratic? [tex] f(x) = a(x - h)^2 + k [/tex]

it could be its. a function, if you know what that is. for every x value there is only one y value, yes it is possible it's a quadratic.
 
  • #5
I believe courtrigrad knows what a function is! I suspect his original response was asking whether you know what a quadratic is!:smile:
 

FAQ: Solve Quadratic Equation Given Roots & Point

What is a quadratic equation?

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.

How do you find the roots of a quadratic equation?

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.

What does it mean to solve a quadratic equation given roots and a point?

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.

Can you have more than two roots for a quadratic equation?

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.

How do you check if a given point is a solution to a quadratic equation?

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.

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