Intro to Quadratics

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form y = ax² + bx + c, where a, b, and c are constants.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

How do you find the vertex of a quadratic function?

Back

The vertex can be found using the formula x = -b/(2a) and then substituting x back into the function to find y.

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).

Front

What are x-intercepts?

Back

X-intercepts are the points where the graph of a function crosses the x-axis, found by setting y = 0 and solving for x.

Front

What is the significance of the coefficient 'a' in a quadratic function?

Back

The coefficient 'a' determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

What is the difference between a minimum and maximum in a quadratic function?

Back

A minimum is the lowest point of the parabola (opens upwards), while a maximum is the highest point (opens downwards).

Front

How do you determine if a quadratic function has a minimum or maximum?

Back

If the coefficient 'a' is positive, the function has a minimum; if 'a' is negative, it has a maximum.

Front

What is the formula for finding the y-coordinate of the vertex?

Back

The y-coordinate of the vertex can be found by substituting x = -b/(2a) into the quadratic function.