Looking at y=ax2+c
Ex.#1 Graph each set of parabolas on the TI­83 and transfer them on to grid provided.
Part 1.
y=­x2
y=­x2+4
C= height of vertex when (no b value)
a= + opens up a= ­ opens down
a>1 = stretched (ignore (­) sign here)
a<1= compressed (ignore (­) sign here)
Part 2.
y=­x2
y=­2x2+4
stretched by a factor of 2
Part 3.
y=­x2
y=­(1/2)x2+4
compressed by a factor of 0.5
Ex.#2 The arches in Nathan Phillips Square go over top an ice rink.
a)Determine the equation that can represent the arches. If the vertex is located on the y­axis, we can say the equation of the parabola would be y=ax2+c.
b) If the scale of the grid is 1 unit represents 2m, determine the height and width of the arch.
Ex.#3 The Gateway Arch in St.Louis is roughly 192m high and 192m
wide. Determine the equation of a parabola that can represent
the arch.
Ex.#4 The parabolic equation for the one of the arches of the giant McDonald's sign can be represented by the equation
y=-0.2x2+20.
a) What is the height of the arch?
b) What is the width of the one arch?
HOMEWORK
sheet
Ex.#3 The Gateway Arch in St.Louis is roughly 192m high and 192m
wide. Determine the equation of a parabola that can represent
the arch.
Ex.#4 The parabolic equation for the one of the arches of the giant McDonald's sign can be represented by the equation
y=-0.2x2+20.
a) What is the height of the arch?
b) What is the width of the one arch?
HOMEWORK
sheet
1. Each arch in the BCE Place Galleria can be approximated by the equation y=-0.55x2+26, where y is the height, in metres, above the floor and x is the width, in metres, from the centre of the hallway.
a) Determine the vertex of the arch.
b) Determine the height of the arch.
c) Determine the width of the arch.
2. The Rainbow Bridge in Utah is a natural stone bridge. It has a parabolic shape and the equation to represent it is h=-0.0159d2+290, where h is the height and d is the width, both in feet.
a) Determine the vertex of the bridge. b) Determine the height of the bridge.
c) Determine the width of the bridge.
3. The Ambassador Bridge connects Detroit to Windsor over the Detroit River. The width between two towers is 564m apart and the height of the tower is 72m. Determine a parabolic equation that can represent the cable between the two towers.
564m
72m
4. How does the value of a in y=ax2+c affect the graph? Include negative values, positive values and fractional values of a.
ANSWERS:
1a) V=(0,26) b) 26m c) 13.75m 2a) V=(0,290) b) 290m c) 270.1m
3. h=0.000905d2+72
4. If a is negative, the graph opens down. If a is positive, the graph opens up. If a is number bigger than 1 (fraction included), the parabola is stretched; meaning it gets longer and skinnier, like stretching an elastic band. If a is a fraction less than one, the parabola is compressed; meaning it gets shorter and fatter, like squishing a marshmallow.
Attachments
Day1Sheet_MCR3U_Fall 2010
Day1Rubrics_MCR3U
MCR3U_Day1Sheet_Fall 2011.doc
MCR3U_Day1Rubrics.doc
MCR3U_outline_unitbyunit_fall2011.doc
Day1Sheet_Fall2010.docx
Day1Rubrics.docx
MFM2P_outline_unitbyunit_Fall2010.docx