Finding the Equation of a Parabola

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SUMMARY

The discussion focuses on finding the equation of a quadratic function that passes through the points (-2,1), (-6,1), and (2,-7). The method involves solving the system of equations derived from the standard form of a quadratic equation, \(y = ax^2 + bx + c\). Additionally, the vertical line of symmetry is identified at \(x = -4\), which aids in using the vertex form \(y = a(x-h)^2 + k\) to determine the constants \(a\) and \(k\). This approach effectively combines both standard and vertex forms to derive the quadratic equation.

PREREQUISITES
  • Understanding of quadratic functions and their properties
  • Familiarity with solving systems of equations
  • Knowledge of vertex form of a quadratic equation
  • Ability to manipulate algebraic expressions
NEXT STEPS
  • Practice solving quadratic equations using the vertex form
  • Explore the concept of symmetry in parabolas
  • Learn about the implications of the discriminant in quadratic equations
  • Investigate graphical methods for finding quadratic equations
USEFUL FOR

Students studying algebra, educators teaching quadratic functions, and anyone interested in mastering the techniques for deriving equations of parabolas from given points.

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Find the equation of a quadratic function whose graph contains the given points.
(-2,1), (-6,1), (2,-7)

THANK YOU
 
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Find the equation of a quadratic function whose graph contains the given points.
(-2,1), (-6,1), (2,-7)

solve the system for $$y = ax^2+bx+c$$ ...

$a(-2)^2 + b(-2) + c = 1$

$a(-6)^2 + b(-6) + c = 1$

$a(2)^2 + b(2) + c = -7$
 
One other method ... note the two coordinates with the same y-value.

a parabola's vertical line of symmetry would pass through the midpoint of those two points, i.e. $x=-4$

using the vertex form for a quadratic equation, $y=a(x-h)^2+k$, the vertex is at the coordinates $(h,k)$.

so, you know $h=-4$ and you have three sets of coordinates ... you should be able to substitute those values to determine the constants $a$ and $k$.
 

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