Quadratic & Polynomial Graphs Flashcards

All 7 cards in this deck

What are the coordinates of the point where the curve $y = ax^2 + bx + c$ crosses the $y$-axis?

e.g. $y = x^2 + 2x - 5$

$(0, c)$ — substitute $x = 0$.

e.g. $(0, -5)$

What are the coordinates of the turning point of $y = a(x - p)^2 + q$?

e.g. $y = 4 - (x - 3)^2$

$(p, q)$

e.g. maximum point $(3, 4)$

What is the equation of the line of symmetry of $y = a(x - p)^2 + q$?

e.g. $y = 2(x + 1)^2 - 7$

$x = p$

e.g. $x = -1$

True or false? The graph of $y = 2x^2 - 8x + 1$ has a maximum point.

False. The coefficient of $x^2$ is positive, so the curve is U-shaped and has a minimum point.

What are the steps to sketch a quadratic, labelling its intersections with the axes?

e.g. $y = x^2 - 4x + 3$

1. Shape from the $x^2$ coefficient: positive, so U-shaped.
2. $x = 0$ for the $y$-intercept: $(0, 3)$.
3. $y = 0$ for the roots: $(1, 0)$ and $(3, 0)$.

What is a piecewise-defined function?

A function given by a different rule on each of two or more separate domains (intervals) of $x$.
e.g. $y = 2x$ for $0 \le x \le 2$ and $y = 4$ for $2 < x \le 5$

What are the steps to draw the graph of a piecewise-defined function?
e.g. $y = 2x$ for $0 \le x \le 2$, then $y = 4$ for $2 < x \le 5$

1. Work out the end values of each piece: $(0,0)$ and $(2,4)$; then $(2,4)$ and $(5,4)$.
2. Draw each rule only across its own domain: line from $(0,0)$ to $(2,4)$, then a horizontal line to $(5,4)$.
3. Draw nothing outside the given domains.