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in this example were going to take a look at these three ordered pairs and we would like to write a quadratic function whose graph passes through well these three ordered pairs and so a quadratic function will be in the form if its in standard form a x squared plus b x plus c okay well i can use this information right here and each one of these ordered pairs in succession to build a really nice system of equations which then we can solve and what well be solving for are the values of a b and c these coefficients and so then i can write them in and ill have a nice function and so we know that this f of x can be replaced by a y so well have y equals ax squared plus bx plus c so lets go ahead and take each one of our ordered pairs and well start with negative 2 5. well the negative 2 is my x value the 5 is my y value so lets go ahead and write an equation so y well thats my 5 equals a and my x squared well thats negative 2 squared plus b and times x plus c so when i polish this