Solve Quadratic Equation Given Roots & Point

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To find the standard form of a quadratic equation given the roots -2 and 8, the equation can be expressed as f(x) = a(x + 2)(x - 8). The intersecting point provided is (-1, 16), which is used to determine the value of 'a' by substituting these coordinates into the equation. The discussion confirms that the equation is indeed a quadratic function, as it adheres to the definition of having one output (y value) for each input (x value). The main focus is on calculating the correct value of 'a' to satisfy the given point. Understanding the relationship between the roots, the point, and the quadratic form is essential for solving the problem.
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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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Is this a quadratic? f(x) = a(x - h)^2 + k
 
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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?
 
courtrigrad said:
Is this a quadratic? f(x) = a(x - h)^2 + k

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.
 
I believe courtrigrad knows what a function is! I suspect his original response was asking whether you know what a quadratic is!:smile:
 
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