Understanding Adding and Subtracting Rational Expressions

This video introduces quadratics, explaining their standard form and how they graph into parabolas. It covers the axis of symmetry and vertex, providing examples to illustrate these concepts. The video also demonstrates using a graphing calculator to sketch quadratics and solve problems.

What is the standard form of a quadratic equation?

• y = ax + bx + c

• y = ax^3 + bx + c

• y = ax^2 + bx^2 + c

• y = ax^2 + bx + c

What shape does the graph of a quadratic equation form?

• An ellipse

• A parabola

• A circle

• A straight line

If the coefficient 'a' in a quadratic equation is positive, how does the parabola open?

• To the right

• To the left

• Downwards

• Upwards

What is the axis of symmetry in a parabola?

• A horizontal line dividing the parabola

• A curved line dividing the parabola

• A vertical line dividing the parabola

• A diagonal line dividing the parabola

What is the formula for the axis of symmetry?

• x = b / a

• x = -b / 2a

• x = b / 2a

• x = -b / a

What do we call the turning point of a parabola?

• Directrix

• Axis

• Focus

• Vertex

If the vertex of a parabola is at its lowest point, what is it called?

• Minimum

• Directrix

• Maximum

• Focus

For the quadratic equation y = x^2 + 8x + 15, what is the axis of symmetry?

• x = 4

• x = -4

• x = -8

• x = 8

For the quadratic equation y = -x^2 + 10x - 23, what is the vertex?

• (-5, -2)

• (5, 2)

• (5, -2)

• (-5, 2)

If a quadratic equation has no 'bx' term, what is the axis of symmetry?

• x = -1

• x = 0

• x = -2

• x = 1