Finding the Vertex
What's the vertex of the given quadratic:
y=-3(x+6)^2+5
Vertex = (-6,5)
In order to check for the number of solutions, we check this part of the quadratic formula
What is the discriminant
b^2-4ac
Put the following in simplest radical form:
√27
3√3
Solve for x:
0=2x^2-32
x={-4, 4}
A projectile is launched into the air from the ground with an initial velocity of 400 feet per second. Write the quadratic that would model the projectile's height after t seconds
h(t)=-16t^2+400t
Find the vertex of the quadratic in factored form:
y=-2(x-3)(x+7)
Vertex = (-2,50)
How many solutions?
0=x^2-6x+9
1 solution
Put the following in simplest radical form:
4√76
8sqrt19
Solve for x:
y=3x^2+13x-10
x={-5, 2/3}
A projectile is launched into the air from the ground with an initial velocity of 400 feet per second. Find the time it takes to reach its peak
t=12.5 seconds
What's the range of the following quadratic?
y= -16(x-4)^2+225
y ≤ 225
How many solutions?
7=3x^2+9x+14
No solutions
Put the following in simplest radical form:
sqrt((-4)^2-4(1)(-8))
4sqrt3
Solve for x:
0=-2(x+6)^2+32
x={-10, -2}
A company is changing it's pricing model to try and maximize profits. The proposed changes can be modeled by the formula below, where x = # of price increases. (500+30x) is the price after x increases, (250-25x) is the change in sales after x increases. How many increases would result in the company "breaking even"? (profits=0)
Profits= (500+30x)(250-25x)
x=10 or "after 10 price increases"
Write the following in Vertex Form by completing the square and then identify the vertex:
y= x^2+14x-3
In vertex form:
y=(x+7)^2-52
Vertex = (-7,-52)
How many solutions?
y=x^2-1
y=-2x^2+5x-7
No solutions
Put the following in simplest radical form:
(-6±sqrt((-6)^2-4(-1)(41)))/(2(-1)
3±5sqrt2
Solve for x in simplest radical form:
0=-16x^2-48x+72
x={(-3+3sqrt3)/2, (-3-3sqrt3)/2}
A landscaping company wants to build a walkway around a garden. The garden is currently 15ft x 20ft. Their permit allows the garden + walkway to take up a total of 546 sq ft. How wide will the walkway need to be if it's uniform on all sides?
3 feet