Week 9 – Precalc 11

This week in Precalculus 11, we learned about equivalent forms of a quadratic function.

quadratic function:

x-intercept: point on a graph crossing the x-axis

root: x-value to an equation when solved

y-intercept: point on a graph crossing the y-axis

vertex: maximum (opening down) or minimum (opening up) point on a parabola

A quadratic function has 3 forms: factored, general, and standard.

factored form: y = a(x – x_1)(x – x_2)

  • x_1 & x_2 are the graph’s x-intercepts, or the equation’s roots

general form: y = ax^2 + bx + c

  • c is the graph’s y-intercept

standard form: y = a(x - p)^2 + q

  • p is the vertex’s x-value
  • q is the vertex’s y-value

For all 3 forms, a determines whether the parabola opens up (positive) or down (negative) and its stretch (a>1) or compression (a<1) value.

By converting from one form to another, we can determine all elements of the equation.

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