Algebraic Reasoning Fall Sem Review

Front

What is the expanded form of the equation y = (3x − 6)(7x + 7)?

Back

21x² − 21x − 42

Front

What are the roots of the quadratic equation 3x² - 12x + 9 = 0?

Back

x = 3, x = 3

Front

Identify the coefficients a, b, and c in the equation 4x² – 8x = 3.

Back

a = 4, b = -8, c = -3

Front

What is the value of the discriminant for the parabola described by the equation 2x² - 4x + 1 = 0?

Back

8

Front

Does the ball reach a maximum or minimum height in the equation y = -4x²?

Back

maximum

Front

What is a parabola?

Back

A parabola is a symmetric curve formed by the intersection of a cone with a plane parallel to its side.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0, where a, b, and c are constants.

Front

What does the discriminant of a quadratic equation indicate?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if > 0, two distinct real roots; if = 0, one real root; if < 0, no real roots.

Front

How do you find the vertex of a parabola given in standard form?

Back

The vertex can be found using the formula (-b/2a, f(-b/2a)).

Front

What is the axis of symmetry for a parabola in standard form?

Back

The axis of symmetry is the vertical line x = -b/2a.