Algebra II A Unit 4

Front

What are the values of a, b, and c in the quadratic equation 4x² - 8x - 3 = 0?

Back

a = 4, b = -8, c = -3

Front

Does the graph of a quadratic function have a maximum or minimum value?

Back

It can have either a maximum or minimum value depending on the direction of the parabola. If it opens upwards, it has a minimum value; if it opens downwards, it has a maximum value.

Front

How do you determine the solutions of a quadratic equation from its graph?

Back

The solutions (or roots) of the quadratic equation are the x-intercepts of the graph.

Front

Find the solutions to the polynomial equation x² - 8x = 9.

Back

The solutions are {-1, 9}.

Front

What are the zeros of the function f(x) = (x + 4)(x - 3)(x - 2)?

Back

The zeros are x = -4, x = 3, x = 2.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0, where a, b, and c are constants.

Front

What does the vertex of a parabola represent in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola.

Front

How can you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula x = -b/(2a) and then substituting x back into the function to find y.

Front

What is the quadratic formula used for?

Back

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

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root: b² - 4ac. It determines the nature of the roots.