Algebra 1: Quadratic Functions and Parabolas

Study Notes

Quadratic Functions and Parabolas Study Notes

The axis of symmetry for a quadratic function can be calculated using the formula: ( x = -\frac{b}{2a} ).
The equation to solve and find the roots of a quadratic equation is given by the quadratic formula: ( y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ).
To find the vertex of a quadratic function represented as ( ax^2 + bx + c ), substitute the ( x ) value back into the equation to get the corresponding ( y ) value.
The axis of symmetry ensures that both sides of the parabola are mirror images; if this is not true, it indicates an error in calculations.
The vertex of a parabola is the minimum or maximum point located on the axis of symmetry, essential for determining the parabola's direction.
The direction in which a parabola opens (upward or downward) depends on the coefficient of ( x^2 ):
- If positive, the parabola opens upwards.
- If negative, it opens downwards.
The roots of a quadratic function represent the points where the graph intersects the x-axis, also known as the x-intercepts.
The discriminant of a quadratic equation determines the nature of the roots:
- Two distinct real roots when positive,
- One real root (double root) when zero,
- No real roots when negative.
In the formula ( h = -16t^2 + vt + s ):
- ( H ) represents the initial height,
- ( T ) indicates time,
- ( V ) is the initial velocity,
- ( S ) stands for speed.

Description

Test your knowledge of quadratic functions and parabolas with these flashcards. Each card covers key concepts, including the axis of symmetry, solving quadratic equations, and finding the vertex. Perfect for students mastering Algebra 1!