What does it mean for a quadratic to have real zeros?

It means the graph of the quadratic intersects the x-axis.

What is the vertex of a quadratic function?

The vertex is the highest or lowest point on the graph of the quadratic.

What is the axis of symmetry in a quadratic function?

The axis of symmetry is the vertical line $$x = -\frac{b}{2a}$$ .

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

The discriminant $$D = b^2 - 4ac$$ determines the nature of the roots.

If $$D > 0$$ , what can be said about the roots of the quadratic?

There are two distinct real roots.

If $$D = 0$$ , what can be said about the roots of the quadratic?

There is exactly one real root (a repeated root).

There are no real roots (the roots are complex).

Resource Library

Math

Algebra

Zero Product Property

Quadratics Zero Product Property

Quadratics- Zero Product Property

Flashcard

•

Mathematics

•

10th Grade

•

Practice Problem

•

Hard

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FLASHCARD QUESTION

Front

What is the Zero Product Property?

Back

If $a \times b = 0$ , then either $a = 0$ or $b = 0$ .

FLASHCARD QUESTION

Front

How do you find the zeros of a quadratic function?

Back

Set the function equal to zero and solve for $x$ .

FLASHCARD QUESTION

Front

Solve for $x$ : $0 = (2x + 5)(x - 6)$

Back

$x = -\frac{5}{2}, x = 6$ .

FLASHCARD QUESTION

Front

Solve using the Zero Product Property: $\left(3x + 2\right)(x + 1) = 0$

Back

$x = -1, x = -\frac{2}{3}$ .

FLASHCARD QUESTION

Front

Solve: $r(r + 7) = 0$

Back

$r = 0, r = -7$ .

FLASHCARD QUESTION

Front

Solve: $0 = x(x - 6)$

Back

$x = 0, x = 6$ .

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

The standard form is $y = ax^2 + bx + c$ .

10.

FLASHCARD QUESTION

Front

How can you determine the direction of a parabola?

Back

If $a > 0$ , the parabola opens upwards; if $a < 0$ , it opens downwards.

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