Quadratics
What is the standard form for a quadratic equation?
What is ax2 + bx + c?
What are the three trigonometric ratios for a right triangle?
What are sine, cosine, and tangent (soh, cah, toa)?
What do you call a set of lines that have the same slope yet different y-intercepts?
What are parallel slopes?
The midsegments of any quadrilateral can be joined to form?
What is a parallelogram?
What is x2+ y2 = r2 ?
What one value cannot a (in the standard form equation) be if the equation were to be quadratic?
What is zero?
What law of a non-right triangle indicates that the ratio of a length of the side to its opposite angle is constant throughout all three sides?
What is sine law?
If a linear system has different equivalent slope and same y-intercept, how many solutions will it have?
What is one solution? (The solution is the y-intercept!)
True or False? The medians of a triangle bisect ALL areas of a triangle?
What is True?
If Trans Canada Highway (BC 1), runs through Vancouver, the Lower Mainland, and the Pacific Coastline from the Alberta Border (85, 10) to Nanaimo on Vancouver Island on British Columbia's coast (- 25, -15), find the length of the highway across British Columbia to the nearest kilometre.
What is (about) 113km? Use the distance formula.
Using a pattern from a table of values, how do you know if a relation is going to be quadratic?
What are constant second differences?
The government is working on building the new Interstate 280 through the San Francisco Bay Area. While at an elevation of the Yosemite mountains of 6 miles, the city of Cupertino is spotted 17 miles away near Apple Park. At what angle of depression should I-280 be constructed so that it would curve towards Cupertino? Round your answer to the nearest degree.
What is (about) 19 degrees?
I-280 should curve about 19 degrees downward towards Cupertino.
What is the point of intersection for the following lines?
3x + 3y = 27
4y = -x + 12
What is (8,1)?
x = 8
y = 1
What is a circumcentre?
What is the concurrency point of the right bisectors of a triangle in the centre of a circle, which intersects all 3 vertices?
True or False: Highway 401's Express Lanes start from Brock Road (399, 14) and end at Highway 6 in Milton (299, 8). As usual, the freeway passes the city of Toronto and is busiest in the mid-length point of express lanes. Highway 427 (the Pearson Airport Expressway) interchanges the 401 at point (349, 10). Is the 401 busiest at the 427 interchange?
Pay attention to the coordinates (349, 10). The midpoint of the express lanes are (349, 11), meaning the busiest part is 1 km north of the 427 interchange.
How many solutions does this equation have?
f(x) = 9x2 - 77x + 105
What are two solutions? (Hint: Use the discriminant!)
An Air Canada plane bound for Vancouver is running low on fuel. There are two nearby airports, Abbotsford International Airport (40 degree angle) and Bellingham International Airport (58 degree angle) that are 240 km apart from each other. Which one is closer for the Air Canada flight to land?
What is Abbotsford International Airport? (about 156km)
True or False? The graph of the equation 2x + 3y = 6 is a straight line that crosses the y-axis with a y-intercept of (0,2).
What is True?
Yes, the y-intercept is 2, so the line crosses the y-axis at (0,2)! Set the value of x to zero to find the y-intercept.
Point A = West Deep End: (-12, 5)
Point B = South Deep End: -12, 0
Point C = East Deep End: (12,7)
What is (-4, 4)? Use the centroid formula!
[(x1 + x2 + x3) divided by 3, (y1 + y2 + y3) divided by 3]
Boundary Road (BC Route 17) runs from the Peace Arch in Blaine, Washington State/Surrey, BC Boundary and goes 4km west for every kilometre north. If zintercept's Richmond, BC office is at the point (-6, 9), what is the shortest distance from the office to Boundary Road (rounded to the nearest tenth of a kilometre)?
What is (about) 7.3 km? Actual: (7.27 km)
What are the axis of symmetry, y-intercept, as well as the solutions for this equation?
f(x) = 9x2 + 1800x + 100
What are? :
Axis of symmetry: x = -100
y-intercept = (0, 100)
Solutions=
x1 = 1/3 and x2 = -601/3
Francis has two types of rope that are 5.3m and 5.9m and intersect together at 89 degrees. A third rope runs along and intersects the rope measuring 5.3m at a 55 degree angle, using this information. How long is the third rope rounded to the nearest metre?
What is 8 metres?
(Using the cosine law)
Joshua is trying to find the exact shade of midnight green to replace his iPhone back glass. He finds two paints, one at 93% saturation, and one at 17% saturation. If he wants to make 100ml of paint at exactly 50% saturation, how much of each paint should he buy (rounded to the nearest mililiter)?
What is about 43ml of the 93% saturation of paint and 57ml of the 17% saturation of paint?
American Airlines Flight 72 is trying to find the location of the Los Angeles Airport Tower to land. The aircraft loses signal at the following locations.
A. Ventura (138 km north of Los Angeles, 18 km west)
B. Malibu (27 km west of his house, 21 km north)
C. Catalina Island (106 km west of his house, 8 km south)
Where is the American Airlines Flight from Los Angeles (to the nearest km in both directions)?
What is 161 km west and 90 km north of Los Angeles?
(-161, 90). Actual answer: (-160.8, and 89.6)
Lifeguards in Granville Island, BC along the Pacific Coast are supposed to do a rotation within their supervision area. Granville Island borders Vancouver's Gastown 24km west and 7 km north of the city centre, where the lifeguards conduct a rescue. Using this point, what is their radius and their total area of supervision (rounded to the nearest kilometre)?
For radius: What is 25km?
Total area of supervision: What is (about) 1963km2?