Quadratic Graphs Flashcards

All 6 cards in this deck

What are the roots of a quadratic graph?

The $x$-coordinates of the points where the curve crosses the $x$-axis, i.e. the solutions of $y = 0$.

How do you find the $y$-intercept of a quadratic from its equation?

e.g. $y = x^2 - 6x + 4$

It is the constant term (the value of $y$ when $x = 0$).
Here the $y$-intercept is $4$, i.e. $(0,4)$.

What is the turning point of a quadratic graph?

The maximum or minimum point, where the curve changes direction; it lies on the line of symmetry.

What is the equation of the line of symmetry of a parabola with turning point $(2,-13)$?

$x = 2$.
The line of symmetry is $x =$ the $x$-coordinate of the turning point.

True or false? Every quadratic graph crosses the $x$-axis twice.

False.
A parabola can cross the $x$-axis twice, touch it once, or not meet it at all.

How can you tell from its equation whether a parabola opens upwards or downwards?

Positive coefficient of $x^2$ opens upwards (minimum); negative coefficient opens downwards (maximum).