Study quadratic graphs, forms, transformations, and modeling.
Common CoreF-IF.C.7aF-BF.B.3A-SSE.B.3
6 lessons21 short videos5 key concepts, out loud
14.1
Characteristics of Parabolas (Vertex / Symmetry)
Vertex, axis of symmetry, and direction
F-IF.C.7a
Key idea
A parabola is a symmetric, U-shaped curve with a single turning point called the vertex, an axis of symmetry that splits it into mirror images, and a direction of opening determined by the sign of its leading coefficient.
Learn how to identify a parabola's vertex, write the equation for its axis of symmetry, and determine whether it opens upward or downward.
Key concept · Lesson 14.1
Vertex first, then the line of symmetry
Listen0:00 / 0:25
Transcript. Every parabola has one turning point, the vertex, written h comma k. The curve is symmetrical, so both sides match across a vertical line through it. Write that line as an equation, x equals h, not just a bare number. Positive a opens up to a minimum, negative a opens down to a maximum.
14.2
Graphing Quadratics in Standard Form
Graph y = ax^2 + bx + c
F-IF.C.7a
Key idea
To graph a quadratic function in standard form, y = ax^2 + bx + c, calculate the axis of symmetry using x = -b/(2a), evaluate this input to find the vertex, and use the y-intercept (0, c) along with symmetric points to plot the parabola.
Learn how to find the axis of symmetry, vertex, and y-intercept of a standard form quadratic equation to sketch its symmetric curve.
Key concept · Lesson 14.2
Center line, then the vertex
Listen0:00 / 0:20
Transcript. Standard form hands you the y-intercept for free: it is the constant c. For the center line, use negative b over two a, and keep that leading minus even when b is already negative. Plug that x back in, with parentheses, to get the vertex height.
14.3
Vertex Form & Transformations
Shift, stretch, and flip a parabola
F-BF.B.3
Key idea
To transform the parent quadratic function f(x) = x^2, use the vertex form f(x) = a(x - h)^2 + k, where h shifts the graph horizontally, k shifts it vertically, and a stretches, compresses, or reflects it.
Learn how to shift, stretch, and flip the graph of a parabola by changing the values of a, h, and k in vertex form.
Key concept · Lesson 14.3
Inside switches, outside keeps
Listen0:00 / 0:22
Transcript. Vertex form shows the turning point directly. The number inside the parentheses switches sign, so x plus four means the vertex sits at negative four. The number outside keeps its sign. A negative leading value flips the curve upside down, and remember to square the binomial.
14.4
Modeling with Quadratics (Projectile Motion)
Height, area, and path problems
A-CED.A.1
Key idea
To model real-world scenarios like projectile motion or maximum area with quadratic functions, use the vertex to find the maximum or minimum value and the x-intercepts to find when the object hits the ground or boundary.
Learn how to write and interpret quadratic equations to solve real-world problems about launched objects, maximum areas, and parabolic paths.
Key concept · Lesson 14.4
The vertex gives time and height
Listen0:00 / 0:19
Transcript. The vertex answers two different questions at once. Its first coordinate is the time the object peaks; its second is the height it reaches. Do not report one for the other. The positive x-intercept is when it lands, so a negative time solution gets thrown away.
14.5
Comparing Forms (Standard / Vertex / Factored)
Switch to whichever form is useful
A-SSE.B.3
Key idea
Quadratic functions can be written in standard, vertex, or factored form, each revealing a different key feature of the parabola (y-intercept, vertex, or x-intercepts) and allowing you to convert between them to find the most useful form for a given problem.
Learn how to convert between standard, vertex, and factored forms of a quadratic function and choose the best form to find a parabola's key features.
Key concept · Lesson 14.5
Each form gives away one feature
Listen0:00 / 0:22
Transcript. Three forms, one parabola. When you expand vertex form, square the binomial first, then multiply by the leading number. Never multiply inside the parentheses. Choose the form that already shows what a question asks for, and remember the leading coefficient stays the same in every form.
14.6
Review & Assessment
Quadratic graphing and feature-reading
Review, practice, quiz and test
Key idea
Review quadratic graphing and feature-reading with targeted practice, a practice test, and a chapter test.
This is one chapter of the climb.
Algebra 1 spans 16 chapters, every lesson taught on video with a key concept you can hear, and Vector on hand to answer questions out loud.
