unit 4 flashcard 4

Front

What is the factored form of a quadratic function?

Back

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

Front

How do you convert a quadratic function to standard form?

Back

To convert a quadratic function to standard form, you can factor the quadratic expression into the form f(x) = (x - p)(x - q), where p and q are the x-intercepts.

Front

What are the solutions of the equation 7x^2 - 26x - 8 = 0?

Back

The solutions are x = 4 and x = -\frac{2}{7}.

Front

How do you find the x-intercepts of a function?

Back

To find the x-intercepts of a function, set f(x) = 0 and solve for x.

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 images, given by the formula x = -\frac{b}{2a} for a quadratic in the form ax^2 + bx + c.

Front

What does the vertex of a parabola represent?

Back

The vertex of a parabola represents the highest or lowest point of the graph, depending on whether it opens upwards or downwards.

Front

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

Back

The leading coefficient determines the direction of the parabola: if it is positive, the parabola opens upwards; if negative, it opens downwards.

Front

How do you determine if a quadratic function has real solutions?

Back

A quadratic function has real solutions if the discriminant (b^2 - 4ac) is greater than or equal to zero.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

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

Back

The sum of the roots (r1 + r2) is equal to -b/a, and the product of the roots (r1 * r2) is equal to c/a.