Algebra 1, Unit 8: Quadratic Functions and Equations. Key terms, formulas, and worked-example cues a high school student meets for this unit, building on prior units. Front: the term, formula name, or short problem cue. Back: the definition, formula, or solution method.
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- What is a quadratic function?
- A function of the form f(x) = ax^2 + bx + c, where a is not zero
- What shape does a quadratic function's graph make?
- A parabola
- What is the vertex of a parabola?
- The highest or lowest point on the graph
- What is the axis of symmetry of a parabola?
- The vertical line through the vertex, dividing the parabola into mirror-image halves
- What formula finds the axis of symmetry (and x-coordinate of the vertex)?
- x = -b / (2a)
- What does it mean if a parabola opens upward?
- The leading coefficient 'a' is positive
- What does it mean if a parabola opens downward?
- The leading coefficient 'a' is negative
- What is the standard form of a quadratic function?
- f(x) = ax^2 + bx + c
- What is the vertex form of a quadratic function?
- f(x) = a(x - h)^2 + k, where (h, k) is the vertex
- What is the quadratic formula?
- x = (-b +/- sqrt(b^2 - 4ac)) / (2a)
- What is the discriminant of a quadratic equation?
- The expression b^2 - 4ac
- What does a positive discriminant indicate about a quadratic equation's roots?
- Two distinct real solutions
- What does a discriminant of zero indicate?
- Exactly one real solution (a repeated root)
- What does a negative discriminant indicate?
- No real solutions (two complex solutions)
- What is a root (or zero) of a quadratic function?
- A value of x where the function equals zero
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