Flashcard: Factored Form Quadratics

Front

What is the factored form of a quadratic equation?

Back

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

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

Front

How do you find the roots of a quadratic equation in factored form?

Back

To find the roots of a quadratic equation in factored form, set each factor equal to zero and solve for x.

Tags

CCSS.HSA-REI.B.4B

Front

What does the term 'zeros' refer to in the context of quadratic functions?

Back

The term 'zeros' refers to the x-values where the graph of the quadratic function intersects the x-axis, also known as the roots.

Tags

CCSS.HSF-IF.C.7D

Front

What is the relationship between the roots and the factors of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero, and they correspond to the factors of the equation.

Tags

CCSS.HSF-IF.C.7C

Front

How can you determine the number of zeros a quadratic function has?

Back

The number of zeros can be determined by analyzing the discriminant (b² - 4ac) of the quadratic equation. If the discriminant is positive, there are two distinct zeros; if it is zero, there is one zero; and if it is negative, there are no real zeros.

Tags

CCSS.HSA-REI.B.4B

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How can you convert a quadratic equation from standard form to factored form?

Back

To convert from standard form (y = ax² + bx + c) to factored form, you can factor the quadratic expression, often using methods like factoring by grouping or applying the quadratic formula.

Front

What is the significance of the leading coefficient in a quadratic equation?

Back

The leading coefficient (a) determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Tags

CCSS.HSF-IF.C.7A

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, and it can be found using the formula x = -b/(2a) for the quadratic equation in standard form.

Tags

CCSS.HSF-IF.C.7A

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants.