Interpreting Standard Form
In the equation y = 3x2 - 5x + 10, this is the y-intercept
What is (0, 10)?
This is the vertex of the function f(x) = (x - 5)2 + 8.
What is (5, 8)?
If a is negative in the vertex form y = a(x - h)2 + k, the vertex represents this type of point.
What is a maximum?
To shift the graph of y = x2 vertically upward by 10 units, you would change the equation to this.
What is y = x2 + 10?
An animated character jumps in a path modeled by h(d) = -(d - 3)2 + 9. This is the horizontal distance (d) where the character reaches their peak.
What is 3 units?
This term in a quadratic equation determines whether the parabola opens upward or downward.
What is the leading coefficient (or a)?
In the vertex form equation y = a(x - h)2 + k, these two letters represent the coordinates of the vertex.
What are h and k?
Does the graph of y = -0.5(x - 1)2 + 10 open upward or downward?
What is downward?
Replacing (x)2 with (x + 4)2 in an equation moves the graph in this direction.
What is left by 4 units?
In a graph showing the area of a rectangle as a function of its width, the x-intercepts usually represent widths that result in this total area.
What is zero?
If a ball is thrown and its height is modeled by h(t) = -16t2 + 20t + 5, this number represents the height from which the ball was originally released.
What is 5 feet?
This is the vertex of the function g(x) = 2(x + 3)2 - 4.
What is (-3, -4)?
Without graphing, identify the maximum value of the function f(x) = -4(x + 10)2 + 15.
What is 15?
To move the vertex of y = (x - 2)2 + 5 to the origin (0, 0), you must apply these two shifts.
What is left 2 and down 5?
If a quadratic model for a profit has a vertex at (500,10000), where x is the price, this is the price that maximizes profit.
What is $500?
To find the exact time a projectile hits the ground, you must look for this specific feature on a graph.
What is the horizontal intercept (or x-intercept/zero)?
This is why "Vertex Form" is often preferred over "Standard Form" when trying to find the maximum or minimum of a function.
What is "because the vertex coordinates are visible directly in the equation"?
Between y = 2x2 and y = 8x2, this graph will appear "narrower" or steeper.
What is y = 8x2?
If you change y = (x - 1)2 + 3 to y = (x - 1)2 - 5, this is the only feature of the graph that changes.
What is the vertical position (or the y-coordinate of the vertex)?
A diver jumps from a platform. if the vertex of her path is (1, 12) where y is height in meters, this is the maximum height she reaches.
What is 12 meters?
When comparing two projectile paths, the one that reaches a higher peak has a larger value for this specific coordinate of the vertex.
What is the y-coordinate?
Change this equation into vertex form: A parabola with a vertex at (0, 0) that has been shifted 7 units right and 2 units down.
What is y = (x - 7)2 - 2?
If a vertex is at (2, 5) and the graph opens downward, this is the range of the function.
What is y <= 5?
A "horizontal shift" is created by adding or subtracting a number inside this part of the vertex form equation.
What is the squared expression (or inside the parentheses)?
If you want to move a projectile's landing spot further to the right without changing its maximum height, you would adjust this value in vertex form.
What is h (the horizontal shift)?