Understanding Quadratic Expressions

This video tutorial explains how to write quadratic expressions in vertex form, highlighting its importance for graphing and solving equations. It provides a step-by-step guide to converting expressions from general form to vertex form, using examples to illustrate the process, including cases with non-unit and negative leading coefficients.

What is the general form of a quadratic expression?

• ax^2 + bx + c

• a(x + b)^2 + c

• a(x - h)^2 + k

• ax + b

Why is the vertex form useful for graphing quadratic equations?

• It simplifies the equation.

• It makes the equation linear.

• It directly shows the vertex of the parabola.

• It eliminates the need for a graph.

What does the sign of 'a' in the vertex form indicate?

• The axis of symmetry.

• The width of the parabola.

• The direction the parabola opens.

• The color of the graph.

What is the first step in converting a quadratic expression to vertex form if the leading coefficient is not 1?

• Add a constant to both sides.

• Factor out the leading coefficient from the x terms.

• Multiply the entire equation by a constant.

• Subtract a constant from both sides.

In the example where a = 1, what value is added to complete the square?

• 49

• 6

• 36

• 12

What is the result of factoring the perfect square trinomial in the example with a = 1?

• (x - 12)^2

• (x + 6)^2

• (x + 12)^2

• (x - 6)^2

When a = 5, what constant is added to complete the square?

• 9

• 6

• 3

• 12

In the example with a = -4, what is the final expression in vertex form?

• -4(x + 1)^2 + 9

• -4(x - 1)^2 + 9

• -4(x + 2)^2 + 5

• -4(x - 2)^2 + 5

What is the purpose of subtracting the value added to complete the square?

• To maintain equality in the equation.

• To find the vertex.

• To change the equation's form.

• To simplify the equation.

In the example with a = 5, what is the final expression in vertex form?

• 5(x + 3)^2 - 57

• 5(x - 3)^2 + 57

• 5(x + 6)^2 - 12

• 5(x - 6)^2 + 12