Mathematics
Grade 10
15 min
Transformations of quadratic functions
Transformations of quadratic functions
What you'll learn
- Identify the operation (addition, subtraction, multiplication, or division) needed to solve a decimal word problem with 80% accuracy.
- Solve 4 out of 5 decimal word problems involving addition and subtraction, showing all work and using correct decimal placement.
- Apply multiplication and division strategies to accurately solve 3 out of 4 decimal word problems.
- Explain the steps taken to solve a multi-step decimal word problem, using mathematical vocabulary, in writing with at least 3 complete sentences.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the parameters a, h, and k in the vertex form of a quadratic function.
Describe the effects of vertical stretches, compressions, and reflections on the graph of y = x^2.
Describe the effects of horizontal and vertical translations on the graph of y = x^2.
Graph a quadratic function in vertex form by applying a sequence of transformations to the parent function.
Write the equation of a transformed quadratic function given its graph or a description of the transformations.
Determine the vertex, axis of symmetry, and direction of opening from an equation in vertex form.
Ever wonder how a basketball player makes a perfect shot or how a bridge arch is designed? 🏀 The secret lies in understanding the elegant, predictable curves of parabolas!
In this...
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Key Concepts & Vocabulary
TermDefinitionExample
Parent FunctionThe simplest form of a function in a family. For quadratics, this is the function to which all transformations are applied.The parent quadratic function is f(x) = x^2. Its graph is a parabola with a vertex at the origin (0, 0).
VertexThe highest or lowest point on a parabola. It is the point where the parabola changes direction.For the parabola y = (x - 2)^2 + 3, the vertex is at the point (2, 3).
Axis of SymmetryA vertical line that passes through the vertex and divides the parabola into two mirror-image halves.For the parabola y = (x - 2)^2 + 3, the axis of symmetry is the vertical line x = 2.
TranslationA transformation that 'slides' every point of a figure or a graph the same distance in the same direction without changing its size or ori...
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Core Formulas
Vertex Form of a Quadratic Function
f(x) = a(x - h)^2 + k
This is the key formula for understanding transformations. The parameters 'a', 'h', and 'k' tell you exactly how the parent function f(x) = x^2 has been transformed. The vertex of the parabola is located at the point (h, k).
The Role of Parameter 'a'
y = a x^2
The parameter 'a' controls vertical dilation and reflection. If a < 0, the parabola is reflected across the x-axis (opens downward). If |a| > 1, the parabola is vertically stretched (appears narrower). If 0 < |a| < 1, the parabola is vertically compressed (appears wider).
The Role of Parameters 'h' and 'k'
(x - h) and + k
The parameters 'h' and 'k' contr...
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Challenging
What is the y-intercept of the function f(x) = -2(x - 3)^2 + 10?
A.(0, 10)
B.(0, -8)
C.(3, 10)
D.(0, -26)
Challenging
The graph of f(x) = a(x - h)^2 + k is transformed to create g(x) = -a(x - (h+2))^2 + (k-3). How does the vertex of g(x) relate to the vertex of f(x)?
A.It is shifted 2 units left and 3 units up.
B.It is shifted 2 units right and 3 units down.
C.It is shifted 2 units left and 3 units down.
D.It is shifted 2 units right and 3 units up.
Challenging
A parabola opens downwards, and its vertex is in Quadrant IV. What must be true about the parameters a, h, and k in its equation f(x) = a(x - h)^2 + k?
A.a > 0, h > 0, k < 0
B.a < 0, h < 0, k < 0
C.a < 0, h > 0, k > 0
D.a < 0, h > 0, k < 0
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Frequently asked questions
What grade level is "Transformations of quadratic functions"?
Transformations of quadratic functions is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Transformations of quadratic functions?
You'll be able to: Identify the operation (addition, subtraction, multiplication, or division) needed to solve a decimal word problem with 80% accuracy; Solve 4 out of 5 decimal word problems involving addition and subtraction, showing all work….
Is "Transformations of quadratic functions" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Transformations of quadratic functions?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.