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Study Guides > College Algebra CoRequisite Course

Summary: Review

Key Concepts
  • Quadratic functions of form f(x)=ax2+bx+cf(x)=ax^2+bx+c may be graphed by evaluating the function at various values of the input variable xx to find each coordinating output f(x)f(x). Plot enough points to obtain the shape of the graph, then draw a smooth curve between them.
  • The vertex (the turning point) of the graph of a parabola may be obtained using the formula (b2a,f(b2a))\left( -\dfrac{b}{2a}, f\left(-\dfrac{b}{2a}\right)\right)
  • The graph of a quadratic function opens up if the leading coefficient aa is positive, and opens down if aa is negative.
  • Quadratic functions may be used to model various real-life situations such as projectile motion, and used to determine inputs required to maximize or minimize certain outputs in cost or revenue models.

Glossary

projectile motion
(also called parabolic trajectory) a projectile launched or thrown into the air will follow a curved path in the shape of a parabola
quadratic function
a function of form f(x)=ax2+bx+cf(x)=ax^2+bx+c whose graph forms a parabola in the real plane
vertex
the turning point of the graph of quadratic function

Licenses & Attributions