Algebra 1 Final

Front

What are the roots of the function represented by the graph shown?

Back

The roots of the function are the x-values where the graph intersects the x-axis. For example, if the roots are -4 and 0, it means the function equals zero at these points.

Front

Find the vertex of f(x) = -x² - 4x + 12

Back

The vertex of a quadratic function in the form f(x) = ax² + bx + c can be found using the formula x = -b/(2a). For this function, the vertex is (-2, 16).

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the roots of a quadratic equation ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

Solve the equation x² + 4x - 32 = 0

Back

The solutions to the equation are x = -8 and x = 4.

Front

Identify the 'b' value in the equation y = 16x² - 8x - 24

Back

The 'b' value in the equation is -8.

Front

What is the standard form of a quadratic equation?

Back

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

Front

How do you find the axis of symmetry for a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a). It is a vertical line that divides the parabola into two mirror images.

Front

What does the discriminant tell you about a quadratic equation?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if it's positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

What is the vertex form of a quadratic function?

Back

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

Front

How do you convert from standard form to vertex form?

Back

To convert from standard form (ax² + bx + c) to vertex form, you can complete the square.