Mathematics
Grade 11
15 min
Identify the direction a parabola opens
Identify the direction a parabola opens
What you'll learn
- Identify the unit fraction represented by a shaded part of a shape divided into equal parts with 80% accuracy.
- Solve word problems involving finding a unit fraction (1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/10) of a whole number up to 20, and show their work using drawings or equations with 70% accuracy.
- Explain what a unit fraction is in their own words, including that the numerator is always 1, with 100% accuracy.
- Apply their understanding of unit fractions to divide a set of objects (up to 12 objects) into equal groups to represent a given unit fraction (1/2, 1/3, 1/4), demonstrating the relationship between the fraction and the number of objects in each group with 80% accuracy.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the orientation (vertical or horizontal) of a parabola by inspecting which variable is squared in its equation.
Determine if a vertical parabola opens upwards or downwards from its standard form (y = ax^2 + bx + c) by analyzing the sign of 'a'.
Determine if a vertical parabola opens upwards or downwards from its vertex form (y = a(x-h)^2 + k) by analyzing the sign of 'a'.
Determine if a parabola opens up, down, left, or right from its conic section form by analyzing the sign of the parameter 'p'.
Differentiate between the rules for vertically-opening parabolas ((x-h)^2 = 4p(y-k)) and horizontally-opening parabolas ((y-k)^2 = 4p(x-h)).
Rearrange a parabola's equation from general form to a standard form to identify...
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Key Concepts & Vocabulary
TermDefinitionExample
Vertical ParabolaA parabola that opens either upwards or downwards, with a vertical axis of symmetry. In its equation, the 'x' variable is squared.y = 2x^2 - 4x + 5
Horizontal ParabolaA parabola that opens either to the left or to the right, with a horizontal axis of symmetry. In its equation, the 'y' variable is squared.x = -y^2 + 3y - 1
Leading Coefficient (a)In the standard or vertex form of a vertical parabola, 'a' is the coefficient of the x^2 term. Its sign determines if the parabola opens up or down.In y = -3x^2 + 7, the leading coefficient 'a' is -3.
Conic Section FormAn equation form that highlights a parabola's geometric properties, including its vertex (h,k) and the parameter 'p'. There are separate fo...
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Core Formulas
Direction Rule for Vertical Parabolas
For equations `y = ax^2 + bx + c` or `(x-h)^2 = 4p(y-k)`:
1. If `a > 0` or `p > 0`, the parabola opens UPWARDS.
2. If `a < 0` or `p < 0`, the parabola opens DOWNWARDS.
Use this rule when you identify that the 'x' variable is squared. The direction depends on the sign of the coefficient of the squared term ('a') or the sign of the parameter 'p'.
Direction Rule for Horizontal Parabolas
For equations `x = ay^2 + by + c` or `(y-k)^2 = 4p(x-h)`:
1. If `a > 0` or `p > 0`, the parabola opens to the RIGHT.
2. If `a < 0` or `p < 0`, the parabola opens to the LEFT.
Use this rule when you identify that the 'y' variable is squared. The direction depends on the sign of the coefficient...
5 more steps in this tutorial
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Challenging
Determine the direction of opening for the parabola `3x^2 + 18x - 6y + 33 = 0`.
A.Upwards
B.Downwards
C.To the right
D.To the left
Challenging
A parabola has the form `(x - h)^2 = 4p(y - k)`. If it is known that `p` is a negative real number, which way must the parabola open?
A.Upwards
B.Downwards
C.To the right
D.To the left
Challenging
Find the direction of opening for the parabola defined by `2y^2 + 8y = 4x - 16`.
A.Upwards
B.Downwards
C.To the right
D.To the left
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What grade level is "Identify the direction a parabola opens"?
Identify the direction a parabola opens is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Identify the direction a parabola opens?
You'll be able to: Identify the unit fraction represented by a shaded part of a shape divided into equal parts with 80% accuracy; Solve word problems involving finding a unit fraction (1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/10) of a whole number up to….
Is "Identify the direction a parabola opens" 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 Identify the direction a parabola opens?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.