Learn how to rewrite an equation from standard to vertex form so we can graph, y=x^2+6x+2

The video tutorial explains how to convert a quadratic equation from standard form to vertex form. It covers the process of creating a perfect square trinomial, factoring it, and simplifying the equation. The tutorial also demonstrates how to graph the equation in vertex form, identify the vertex, and determine the domain and range of the graph.

What is the first step in converting a quadratic equation from standard form to vertex form?

• Subtract a constant from both sides

• Multiply the equation by a constant

• Place parentheses around the first two terms

• Add a constant to both sides

How do you create a perfect square trinomial from the equation x^2 + 6x?

• Subtract 9 from both sides

• Add 3 to both sides

• Add 9 inside the parentheses and subtract 9 outside

• Multiply by 2

What is the result of factoring the perfect square trinomial x^2 + 6x + 9?

• (x + 3)^2

• (x - 6)^2

• (x - 3)^2

• (x + 6)^2

In the vertex form y = (x + 3)^2 - 7, what is the vertex of the parabola?

• (3, 7)

• (-3, -7)

• (-3, 7)

• (3, -7)

Why is vertex form particularly useful when the leading coefficient is 1?

• It changes the domain of the function

• It makes graphing easier without a table of values

• It allows easy identification of the vertex

• It simplifies the equation

What is the domain of a quadratic function in vertex form?

• From the vertex to infinity

• From negative infinity to the vertex

• From negative infinity to infinity

• From zero to infinity

How is the range of a quadratic function in vertex form determined?

• By the x-coordinate of the vertex

• By the leading coefficient

• By the constant term

• By the y-coordinate of the vertex