Key Feature Connections
What is the key feature of a parabola that names a solution to the quadratic function?
x-intercept
What formula can you use to determine the number of solutions to a quadratic function?
b2-4ac
What are the 3 methods that can be used to find solutions to a quadratic function?
x-intercepts on a graph
factoring
the quadratic formula
This formula is to determine the axis of symmetry of a parabola.
x = -b/2a
Solve
8x2+10x-3=0
x = -3/2 and 1/4
or
x = -1.5 and 0.25
If a rocket is launched into the air. What key feature could help determine how long it will take to hit the ground?
x-intercept
Simplify the square root of 68
2 times the square root of 17
A parabola crosses the x-axis at -7 and -3, what are the factors?
(x+7) and (x+3)
The axis of symmetry of a parabola is given by the equation x=-9
What can you conclude about the vertex?
The x coordinate of the vertex is -9
How do you determine solutions if you are given the graph of a quadratic function?
The x-intercepts are the solutions.
How do you determine the y-intercept if you are given the equation of the quadratic function?
The c-value.
Use the discriminant of 2x2+2x+3 to determine the number of solutions.
No real solutions
You are asked to solve x2+84=-25x
What are the a, b, and c value?
a=1, b=25, c=84
A rocket is launched at time 0. It ascends reaching a maximum height of 480 feet, then descends. It lands after 16 seconds. What are the coordinates of the vertex?
(8, 480)
Determine the positive solution to x2+8x-3=0
Round to the nearest hundredth if necessary
x=0.36
A kicker punts a field goal to score 3 points in a football game. What key feature can by used determine how high he kicked the ball?
The vertex
What are the three outcomes for the value of the discriminant and what can be determined about the number of solutions?
the discriminant is <0 means no real solutions
the discriminant is =0 means one solution
the discriminant is >0 means two solutions
Find the factors of 8x2+10x-3
(4x-1) and (2x+3)
A parabola can be modeled by the equation:
f(x)=2x2-16x+35. If the axis of symmetry of the parabola is at x=4
What are the coordinates of the vertex?
(4, 3)
A quadratic function has x and y values as listed below
x -2 -1 0 1 2 3
y 7 3 3 7 15 27
Find the solutions
no real solutions
What does the a value tell you about where the vertex of a parabola will be?
If a>0 the vertex will be a minimum
If a<0 the vertex will be a maximum
You determine that the solution to a quadratic function are 1 and 5. What can you determine about the value of the discriminant?
It is a positive number
If you factor a quadratic function and get x(x-3.5). What are the solutions?
0 and 3.5
A quadratic function has x and y values as listed below
x -2 -1 0 1 2 3
y 7 3 3 7 15 27
What is the vertex?
(-0.5, 2.5)
The total number of chairs in an outdoor pavilion is modeled by f(x)=2x2+4x, where x represents the number of rows of chairs. If there are 336 chairs write an equation that you can solve to determine how many rows there are in the pavilion.
2x2+4x-336=0