Parabolas
How can the a-value change the shape of a parabola?
It changes if it is concave up or down, and it canges how wide or skinny the parabola is.
Is this equation in Vertex Form?
y = -(x - 1)^2 + 4
Yes
What is the b-value in this equation:
y = 2x^2 - 6x - 23
b = -6
True or False:
sqrt(50) = 5*sqrt(2)
True
If the function y = a(x - 2)^2 + 5 passes through the point (12, 3), which a-value is correct:
(i) a = 0.0012 (ii) a = 0.002 (iii) a = 0.3
(iv) None of the above
TBD
How do you find the roots of parabola from the parabola's graph?
Find the x-intercepts - that's it!
What is Vertex Form for a quadratic function?
y(x) = a(x - h)^2 + k
Is this equation in Standard Form:
y = 2x^2 + 3 + 3x
No! The last two terms are switched.
True or False:
sqrt(125)=25*sqrt(5)
False
Find the equation of the parabola whose vertex is (0, 0), passing through (5, 2).
TBD
What are the possible forms for a quadratic equation?
Vertex Form and Standard Form
What is the vertex of this parabola?
y = -2(x + 4)^2 + 6
(-4, 6)
y = ax^2 + bx + c
The a-value controls how quickly the parabola rises or drops and if it is concave up or concave down.
Simplify: sqrt(500)
10*sqrt(5)
What is the equation for the area of this figure?
A = d(300 - 2d) OR A = -2d^2 + 300d
Match the parabola with the correct equation:
(i) y = 0.2(x-2)^2 + 48
(ii) y = 0.2(x-4)^2 - 68
(iii) y = 0.2(x-6)^2 + 7
Equation (ii)
How many roots does this parabola have:
y = -(x - 1)^2 + 4
Two
Solve this equation using the Quadratic Formula:
0 = x^2 + 8x - 4
x = -16.94...
x = 0.94...
Simplify:
2*sqrt(6) - 2*sqrt(24)
-2 * sqrt(6)
Find the b-value for this parabola if it passes through (2, 10) and (-1, -2):
y = 2x^2 +bx - 2
b = 2
A football is thrown 4.073 feet off of the ground from the endzone. It reaches its vertex at 50 feet, and 83 yards away from the endzone. The parabola's a-value is 0.02 over 3. An angry fan (bob) who doesn’t want this team to win decides to shoot the ball with a bullet, This is a linear equation: the bullet equation is shot 80 feet off of the ground from right above the endzone (0 yards) and has a slope of -0.6
When do they intercept (use graphing)?
57.325 yards from the endzone, 45.605 feet in the air.
Rearrange this equation into standard form:
y = (x + 2)^2 + 10
y = x^2 + 4x + 14
The area for this square is 145 in^2. Find the length and width for this square and make sure to write out the final answer:
SEE IMAGE
x + 2 = 13.552
x - 1 = 10.551
Simplify: (2*sqrt(50))/2
5*sqrt(2)
What is the equation the parabola with x-intercepts at x = 2 and x = -3, and a y-intercept at y = 5?
y = -2x^2 - 2x + 12