Quadratics
Factor the quadratic expression x2+8x+15
(x+5)(x+3)
A right triangle has one leg of length 8 and the hypotenuse of length 10. Find the length of the other leg.
x = 6
A parabola is represented by the equation
y=-3(x-2)2+5
What does the vertex tell you about the graph? Is it concave up or down?
Concave down. Vertex tells us the halfway point.
Explain why knowing only the lengths of two sides of a triangle doesn’t guarantee that the triangles are similar. Give an example.
The third sides may not follow the same proportion
Factor the quadratic expression 2x2+17x+21
(x+7)(2x+3)
A triangle has angles of 30°, 60°, and 90°. If the hypotenuse is 12 inches, find the lengths of the other two sides.
6 inches and 10.4 inches
Are the following two expressions equivalent? Justify your answer: (x+4)(x−2) and x2+6x-8
No, because...
You have two similar right triangles. The first has side lengths of 3, 4, and 5, and the second has side lengths of 6, 8, and 10. What can you conclude about their similarity?
They are similar due to the SSS ratio, where they have a scale factor of 2.
Multiply/FOIL and simplify (x-3)(x+5)
x2+2x-15
You are building a ramp and want it to have a slope of 1:5. If the horizontal length of the ramp is 20 ft, how high will the ramp rise?
4 feet
A function is written as f(x)=x2−4x+3. How many real solutions does this function have? What does this tell you about the graph’s intersection with the x-axis?
Two solutions (x = 1 and x = 3). The graph crosses in the positive quadrant.
What does sin, cos, and tan represent?
They are functions that relate two sides of the triangle. Continue to give detail about each one.
Complete the square to rewrite the quadratic expression in vertex form: x2+10x+9
(x+5)2-16
Use the trigonometric ratios to find the missing side of the triangle: Opposite = 7, Hypoteneuse = ?, Angle = 40°
10.9
The quadratic formula tells you an equations solutions. What would the solutions to this equation be? x2+x++1
No solutions
Solve using the quadratic formula: 2x2-4x-3
x = 2.58 and x = -0.58
Find the angle of elevation to the top of a building if the height is 40 meters and the distance from the base is 50 meters.
38.66º