quadratics features

Front

What are the zeroes of the quadratic equation represented by the factors (x+7)(x+4)?

Back

The zeroes are -7 and -4.

Front

Simplify the expression (a^5)(a^4).

Back

The simplified expression is a^9.

Front

What does it mean if a quadratic graph has a minimum value?

Back

It means the vertex of the parabola is the lowest point on the graph.

Front

Using the quotient rule, simplify the expression 2^{14}z^{13} / z^7.

Back

The simplified expression is 2^{14}z^6.

Front

How do you determine the roots of a quadratic function from its graph?

Back

The roots are the x-coordinates where the graph intersects the x-axis.

Front

What is the standard form of a quadratic equation?

Back

The standard form 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 orientation.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves.

Front

What is the discriminant in a quadratic equation and what does it indicate?

Back

The discriminant is b^2 - 4ac; it indicates the nature of the roots (real and distinct, real and equal, or complex).

Front

What is the factored form of a quadratic equation?

Back

The factored form is y = a(x - r1)(x - r2), where r1 and r2 are the roots.