Algebra 2: Graphing Parabolas Vertex Form

Questions and Answers

What is the quadratic formula written in vertex form?

y = a(x-h)² + k

In the quadratic formula in vertex form y = a(x-h)² + k, what does 'a' represent?

the slope to the point one unit from the vertex

Given the quadratic formula in vertex form y = a(x-h)² + k, how do you find the vertex?

(h, k)

In the quadratic formula in vertex form y = a(x-h)² + k, what does 'h' represent?

the point on the x axis with the axis of symmetry (the origami folding point) Signup and view all the answers

In the quadratic formula in vertex form y = a(x-h)² + k, what do 'h' and 'k' represent?

the vertex Signup and view all the answers

Given the quadratic formula in vertex form y = a(x-h)² + k, how do you find the axis of symmetry?

it is h Signup and view all the answers

Given the quadratic formula in vertex form y = a(x-h)² + k, how do you find the slope to a point one unit from the vertex?

it is a Signup and view all the answers

Given the quadratic formula in vertex form y = a(x-h)² + k, how do you find the y-intercept?

substitute 0 in for 'x' and solve Signup and view all the answers

What is the quadratic formula written in standard form?

y = ax² + bx + c Signup and view all the answers

Given the quadratic formula in vertex form, if 'a' is positive, is the vertex a maximum or minimum?

min Signup and view all the answers

Given the quadratic formula in vertex form, if 'a' is negative, is the vertex a maximum or minimum?

max Signup and view all the answers

Given the quadratic formula in vertex form y = a(x-h)² + k, what information do you need to find in order to graph the parabola?

axis of symmetry, vertex, slope to the point one unit from the vertex, and the y-intercept Signup and view all the answers

Study Notes

Quadratic Formula in Vertex Form

The quadratic formula in vertex form is expressed as y = a(x-h)² + k.

Components of the Vertex Form

"a" indicates the slope to the point one unit from the vertex, determining the width and direction of the parabola.
"h" represents the x-coordinate of the vertex and defines the axis of symmetry of the parabola.
"k" denotes the y-coordinate of the vertex, providing the vertical position of the parabola's turning point.

Vertex

The vertex of the parabola can be found at the coordinates (h, k).

Axis of Symmetry

The axis of symmetry is located at h, which is a vertical line that divides the parabola into two mirror-image halves.

Slope and Points

To find the slope to a point one unit from the vertex, use the value of a.

Y-Intercept Calculation

The y-intercept can be determined by substituting 0 for x in the vertex form equation and solving for y.

Standard Form Comparison

The standard form of a quadratic equation is represented as y = ax² + bx + c.

Min/Max Characteristics

If a is positive, the vertex indicates a minimum point on the graph.
If a is negative, the vertex indicates a maximum point on the graph.

Graphing Information

To accurately graph a parabola in vertex form, identify the following:
- Axis of symmetry
- Vertex
- Slope to a point one unit from the vertex
- Y-intercept

Description

Test your knowledge on graphing parabolas in vertex form with this flashcard quiz. Learn about key concepts such as the quadratic formula, the significance of 'a', and how to find the vertex of a parabola. Perfect for Algebra 2 students looking to reinforce their understanding.