Basic Quadratic Knowledge
What is the standard form of a quadratic function?
What is the standard form of a quadratic function?
Answer: y = ax^2 + bx + c
Graph y = x^2 + 3. What kind of shift is this?
Graph y = x^2 + 3. What kind of shift is this?
Answer: Vertical shift up 3 units
What does the negative in y = -x^2 do?
What does the negative in y = -x^2 do?
Answer: Reflects the parabola over the x-axis
Write y = x^2 + 6x + 8 in vertex form.
Write y = x^2 + 6x + 8 in vertex form.
Answer: y = (x + 3)^2 - 1
The height of a ball is modeled by h(t) = -t^2 + 6t + 2. What is the maximum height?
The height of a ball is modeled by h(t) = -t^2 + 6t + 2. What is the maximum height?
Answer: Vertex: t = 3, height = 11
Identify the vertex of y = x^2.
Identify the vertex of y = x^2.
Answer: (0,0)
Graph y = (x - 2)^2. What kind of shift is this?
Graph y = (x - 2)^2. What kind of shift is this?
Answer: Horizontal shift right 2 units
How does y = 2x^2 differ from y = x^2?
How does y = 2x^2 differ from y = x^2?
Answer: Vertical stretch by factor of 2
Identify the vertex in y = 2(x - 1)^2 + 5.
Identify the vertex in y = 2(x - 1)^2 + 5.
Answer: (1,5)
A parabola has vertex at (2,-3). Write equation in vertex form assuming it opens upwards.
A parabola has vertex at (2,-3). Write equation in vertex form assuming it opens upwards.
Answer: y = a(x - 2)^2 - 3, a>0
What is the axis of symmetry of y = x^2 + 4x + 3?
What is the axis of symmetry of y = x^2 + 4x + 3?
Answer: x = -2
If y = (x + 5)^2 - 4, describe the transformation.
If y = (x + 5)^2 - 4, describe the transformation.
Answer: Shift left 5 units, down 4 units
How does y = 1/3 x^2 differ from y = x^2?
How does y = 1/3 x^2 differ from y = x^2?
Answer: Vertical compression by factor of 1/3
Determine if y = -x^2 + 4x - 3 opens up or down.
Determine if y = -x^2 + 4x - 3 opens up or down.
Answer: Opens down
f(x) = -(x - 1)^2 + 5 represents a fountain’s water. What is the the highest point?
f(x) = -(x - 1)^2 + 5 represents a fountain’s water. What is the highest point?
Answer: Vertex (1,5)
Determine the y-intercept of y = 2x^2 - 3x + 5.
Determine the y-intercept of y = 2x^2 - 3x + 5.
Answer: 5
Given y = (x - 3)^2 + 7, find the vertex.
Given y = (x - 3)^2 + 7, find the vertex.
Answer: (3,7)
Graph y = -3(x + 1)^2 + 2. List all transformations.
Graph y = -3(x + 1)^2 + 2. List all transformations.
Answer: Shift left 1, up 2, vertical stretch by 3, reflected over x-axis
Convert y = 3x^2 - 12x + 7 to vertex form.
Convert y = 3x^2 - 12x + 7 to vertex form.
Answer: y = 3(x - 2)^2 - 5
Toy rocket’s height: h(t) = -5(t - 2)^2 + 20. At what times is height 15?
Toy rocket’s height: h(t) = -5(t - 2)^2 + 20. At what times is height 15?
Answer: t = 1, 3
If a > 0, does the parabola open upwards or downwards?
If a > 0, does the parabola open upwards or downwards?
Answer: Upwards
Write an equation for a parabola with vertex at (-2,5) and opening upwards.
Write an equation for a parabola with vertex at (-2,5) and opening upwards.
Answer: y = (x + 2)^2 + 5
Given y = -1/2(x - 4)^2 - 3, describe vertex, reflection, stretch/compression, and shifts.
Given y = -1/2(x - 4)^2 - 3, describe vertex, reflection, stretch/compression, and shifts.
Answer: Vertex at (4,-3), reflected over x-axis, vertical compression by 1/2, shift right 4, down 3
Explain how y = -2(x + 1)^2 + 4 is transformed from y = x^2.
Explain how y = -2(x + 1)^2 + 4 is transformed from y = x^2.
Answer: Reflected over x-axis, vertical stretch by 2, shifted left 1, up 4
Satellite dish: y = 0.5x^2. Shift up 4 units and stretch by 3?
Satellite dish: y = 0.5x^2. Shift up 4 units and stretch by 3?
Answer: y = 1.5x^2 + 4