Mathematics
Grade 10
15 min
Characteristics of quadratic functions
Characteristics of quadratic functions
What you'll learn
- Identify the correct operation (addition, subtraction, multiplication, or division) needed to solve a word problem with 80% accuracy.
- Solve multi-step word problems involving addition, subtraction, multiplication, and division of whole numbers with 70% accuracy.
- Explain the steps used to solve a word problem, including why each operation was chosen, in a clear and organized manner, using at least two mathematical terms.
- Apply estimation strategies to check if the answer to a word problem is reasonable and explain why the answer is or isn't reasonable.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the vertex of a parabola from its equation in standard or vertex form.
Determine the equation of the axis of symmetry for a quadratic function.
Calculate the x-intercepts (roots/zeros) and the y-intercept of a quadratic function.
Determine the direction of opening (up or down) and identify the maximum or minimum value.
State the domain and range of a quadratic function.
Sketch a graph of a parabola using its key characteristics.
Ever wondered about the perfect arc of a basketball shot or the curve of a satellite dish? 🏀 That's a parabola, and today we're learning its secrets!
This tutorial will guide you through the key features, or characteristics, of quadratic functions. Understanding these properties allows us to graph parabolas ac...
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Key Concepts & Vocabulary
TermDefinitionExample
ParabolaThe distinctive U-shaped curve created by graphing a quadratic function. It can open upwards or downwards.The graph of the function f(x) = x^2 is a parabola that opens upwards with its lowest point at the origin (0,0).
VertexThe highest or lowest point on the parabola. It is the 'turning point' of the curve.For f(x) = (x - 3)^2 + 5, the vertex is at the point (3, 5).
Axis of SymmetryThe vertical line that passes through the vertex and divides the parabola into two perfect mirror images.For a parabola with a vertex at (3, 5), the axis of symmetry is the vertical line with the equation x = 3.
Roots (or Zeros, x-intercepts)The point(s) where the parabola crosses the horizontal x-axis. At these points, the value of the function is zero (f(x) = 0). A par...
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Core Formulas
Standard Form and its Clues
f(x) = ax^2 + bx + c
Use this form to quickly find the y-intercept and direction of opening. The y-intercept is always at (0, c). If 'a' is positive, the parabola opens up. If 'a' is negative, it opens down.
Vertex Form and its Clues
f(x) = a(x - h)^2 + k
This form directly gives you the vertex at the point (h, k). The value of 'a' tells you the direction of opening, just like in standard form.
Axis of Symmetry Formula
x = -b / (2a)
When a quadratic is in standard form (ax^2 + bx + c), this formula gives you the x-coordinate of the vertex, which is also the equation for the axis of symmetry. To find the y-coordinate of the vertex, plug this x-value back into the function.
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Challenging
A parabola has an axis of symmetry at x = 4 and one of its x-intercepts is at (1, 0). What is the coordinate of the other x-intercept?
A.(-2, 0)
B.(7, 0)
C.(5, 0)
D.(4, 0)
Challenging
For what value of 'c' will the quadratic function f(x) = x^2 - 6x + c have exactly one x-intercept?
A.-9
B.0
C.9
D.36
Challenging
What is the sum of the minimum value of f(x) = 2x^2 - 8x + 6 and the maximum value of g(x) = -(x + 1)^2 + 4?
A.2
B.6
C.-2
D.8
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Frequently asked questions
What grade level is "Characteristics of quadratic functions"?
Characteristics of quadratic functions is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Characteristics of quadratic functions?
You'll be able to: Identify the correct operation (addition, subtraction, multiplication, or division) needed to solve a word problem with 80% accuracy; Solve multi-step word problems involving addition, subtraction, multiplication, and division….
Is "Characteristics 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 Characteristics of quadratic functions?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.