Dstermine the equation of function

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SUMMARY

The equation of the quadratic function with an axis of symmetry at x = -1 and passing through the points (0, 3) and (-3, 9) can be expressed in the vertex form $y = a(x + 1)^2 + k$. By substituting the given points into this equation, a system of equations is formed to solve for the coefficients a and k. The analysis reveals two distinct solutions for a, resulting in one parabola opening upwards and another downwards.

PREREQUISITES
  • Understanding of quadratic functions and their properties
  • Familiarity with vertex form of a quadratic equation
  • Ability to solve systems of equations
  • Knowledge of symmetry in graphs
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  • Practice solving quadratic equations in vertex form
  • Explore the concept of parabolas and their characteristics
  • Learn about the implications of the axis of symmetry in quadratic functions
  • Investigate the effects of varying the coefficient 'a' on the graph of a parabola
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Students studying algebra, mathematics educators, and anyone interested in mastering quadratic functions and their graphical representations.

Azurin
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The equation of the axis of symmetry of the graph of a quadratic function is x=-1. The graph passes through the points (0,3) and (-3, 9). Determine the equation of the function.
 
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$y = a(x-h)^2 + k$

you are given $h = -1$

write two equations using the two given (x,y) coordinates and solve the system for $a$ and $k$
 
Azurin said:
The equation of the axis of symmetry of the graph of a quadratic function is x=-1. The graph passes through the points (0,3) and (-3, 9). Determine the equation of the function.
Actually, there are two solutions... one with a = A and one with a = -A. This corresponds to one parabola opening upward and another opening downward.

-Dan
 

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