Quadratic Graphs Flashcards

All 7 cards in this deck

On the graph of a quadratic, where do you read off the roots?

The $x$-values where the curve crosses the $x$-axis.

What is the turning point of a quadratic graph?

The point where the curve changes direction — the minimum point of a U-shape or the maximum point of an n-shape. Written as coordinates, e.g. $(1, -4)$.

What is the $y$-intercept of the graph of $y = x^2 + bx + c$?

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

The constant term $c$ (the value of $y$ when $x = 0$).

For $y = x^2 - 6x + 4$ the $y$-intercept is $4$.

What are the steps to use a quadratic graph to find the values of $x$ for a given $y$?

e.g. find $x$ when $y = 3$

1. Draw a horizontal line at that $y$-value: the line $y = 3$.
2. Mark where this line meets the curve (usually two points).
3. Read straight down to the $x$-axis for each $x$-value.

How do you use a quadratic graph to find the value of $y$ for a given $x$?

e.g. find $y$ when $x = 1.5$

Read up from $x = 1.5$ on the $x$-axis to the curve, then across to the $y$-axis and read off $y$.

True or false? Every quadratic graph crosses the $x$-axis twice, so it always has two roots.

False. A quadratic graph can cross the $x$-axis twice, touch it once, or not reach it at all (no roots).

What is wrong with a quadratic graph drawn with a sharp point at the bottom?

A quadratic curve must be smooth and rounded at the turning point, not pointed.