Quadratic Functions y = ax2
We have discovered through graphing:
The Parent Parabola
y = x2
opens upward
Vertex (minimum point) at (0, 0)
If we graph y
= ax2
(“a“ can be any number: positive, negative, whole numbers, fractions or
decimals)
************************************************************************************
y = -x2
Opens downward
vertex (maximum point) at (0, 0)
Parent parabola is flipped upside down.
*when “a” is a negative number, the parent parabola is flipped upside down.
*****************************************************************************************
y = 2x2
Opens upward
vertex (minimum point) at (0, 0)
Parent parabola is stretched vertically (is narrower) by a factor of 2.
*when “a” is a number greater than 1, the parent parabola is stretched vertically
(narrower). The larger the “a” value, the narrower the parabola.
*******************************************************************************************
y = ½ x2 or y = 0.5x2
Opens upward
vertex (minimum point) at (0, 0)
Parent parabola is compressed vertically (is wider) by a factor of one half.
*when “a” is a number between 0 and 1 (a fraction or a decimal), the parent
parabola is compressed vertically (wider). The smaller the “a” value, the wider
the parabola.
****************************************************************************************
Try These:
1. Which parabolas open downward? Say how you know.
a) y = 12x2
b) y = ⅔ x2
c) y = -4.8x2
d) y = -⅗ x2
2. Imagine the following quadratic functions are graphed on the same x, y axis.
Rewrite the equations in order from widest to narrowest graph.
y = ¼ x2
y = 6x2
y = x2
y = 3.5x2
y = 0.1x2
3. For the following equations, answer the following about the graph
(i) opens up or down
(ii)
the coordinates of the vertex is
(iii)
if it is vertically stretched (narrower) or vertically compressed (wider)
a) y = -0.8x2
b) y = 10x2
c) y = x2
d) y = 0.2x2
4. Write the equation for the graph based on the following descriptions:
a) The parent parabola opens downward and is vertically stretched by a factor
of 3
b) The parent parabola opens upward and is vertically compressed by a factor
of ⅕