Review of Quadratics (part 1)

Front

What does the value of 'a' in a quadratic equation indicate about the parabola?

Back

The value of 'a' determines the direction of the opening of the parabola: if 'a' is positive, the parabola opens upward; if 'a' is negative, it opens downward.

Front

How do you find the axis of symmetry for a parabola given by the equation y = ax^2 + bx + c?

Back

The axis of symmetry can be found using the formula x = -b/(2a).

Front

What are the roots of a quadratic equation?

Back

The roots (or zeros) of a quadratic equation are the values of x that make the equation equal to zero.

Front

Back

x = -1 and x = -3.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax^2 + bx + c.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its direction.

Front

How can you determine the direction a parabola opens from its graph?

Back

If the parabola opens upward, the vertex is the lowest point; if it opens downward, the vertex is the highest point.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: if it's positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

What is another term for the y-intercept of a quadratic function?

Back

The y-intercept is also known as the value of the function when x = 0.

Front

Back

The solutions are x = 3 and x = -2.