Sharp EL9900 manual Slope and Intercept of Quadratic Equations

EL-9900 Graphing Calculator

Slope and Intercept of Quadratic Equations

A quadratic equation of y in terms of x can be expressed by the standard form y = a (x - h) 2+ k, where a is the coefficient of the second degree term (y = ax 2 + bx + c) and (h, k) is the vertex of the parabola formed by the quadratic equation. An equation where the largest exponent on the independent variable x is 2 is considered a quadratic equation. In graphing quadratic equations on the calculator, let the x-variable be represented by the horizontal axis and let y be represented by the vertical axis. The graph can be adjusted by varying the coefficients a, h, and k.

Example

Graph various quadratic equations and check the relation between the graphs and the values of coefficients of the equations.

1. Graph y = x 2 and y = (x - 2) 2.

2. Graph y = x 2 and y = x 2 + 2.

3. Graph y = x 2 and y = 2x 2.

4. Graph y = x 2 and y = - 2x 2.

	Before	There may be differences in the results of calculations and graph plotting depending on the setting.
Starting		Return all settings to the default value and delete all data.
	Step & Key Operation		Display	Notes

1-1		Enter the equation y = x 2 for Y1.
					x2
		Y=	X/ /T/n
1-2		Enter the equation y = (x - 2) 2 for
		Y2 using Sub feature.
			ALPHA		A	(	X/	/T/n	—
				)	x2	+
		ALPHA	H					ALPHA		K
					1			2
		2nd F	SUB			ENTER				ENTER
	( 0				)
			ENTER

1-3View both graphs.

GRAPH

Notice that the addition of -2 within the quadratic operation moves the basic y = x 2 graph right two units (adding 2 moves it left two units) on the x-axis.

This shows that placing an h (>0) within the standard form y = a (x - h) 2 + k will move the basic graph right h units and placing an h (<0) will move it left h units on the x-axis.

4-1