DCA#3 Flashcardizz

Front

What is the distributive property in algebra?

Back

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by two or more terms inside a set of parentheses.

Front

How do you find the vertex of a quadratic function?

Back

The vertex of a quadratic function in the form y = ax^2 + bx + c can be found using the formula x = -b/(2a). Substitute this x-value back into the function to find the y-value.

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. It can be found using the formula x = -b/(2a).

Front

What does it mean for a system of equations to have no solution?

Back

A system of equations has no solution when the lines represented by the equations are parallel, meaning they never intersect.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How do you factor a quadratic expression?

Back

To factor a quadratic expression of the form ax^2 + bx + c, find two numbers that multiply to ac and add to b. Rewrite the expression using these numbers.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation and is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

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

Back

The discriminant, given by b² - 4ac, determines the nature of the roots of the quadratic equation. If it's positive, there are two real solutions; if zero, one real solution; if negative, no real solutions.

Front

What is a parabola?

Back

A parabola is the graph of a quadratic function. It is a U-shaped curve that can open upwards or downwards depending on the sign of the coefficient a in the quadratic equation.

Front

How do you determine the y-value of the vertex from a quadratic function?

Back

To find the y-value of the vertex, substitute the x-value of the vertex (x = -b/(2a)) back into the quadratic function.