A2 Midterm Review #3

Front

Find the vertex of the quadratic function: f(x) = -x^2 - 4x + 12.

Back

The vertex can be found using the formula: x = -b/(2a). Here, a = -1 and b = -4. Thus, x = -(-4)/(2*-1) = -2. To find the y-coordinate, substitute x back into the function: f(-2) = -(-2)^2 - 4(-2) + 12 = 16. Therefore, the vertex is (-2, 16).

Front

What is the vertex for the function: f(x) = 4(x-2)^2 + 3?

Back

The vertex form of a quadratic function is f(x) = a(x-h)^2 + k, where (h, k) is the vertex. Here, h = 2 and k = 3, so the vertex is (2, 3).

Front

Describe the end behavior of the graph of a quadratic function.

Back

For a quadratic function in the form f(x) = ax^2 + bx + c: If a > 0, as x → ∞, y → ∞ and as x → -∞, y → ∞. If a < 0, as x → ∞, y → -∞ and as x → -∞, y → -∞.

Front

The parabola y = -2x^2 - 4x + 1 will open in which direction?

Back

The parabola opens downwards because the coefficient of x^2 (which is -2) is negative.

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 and a ≠ 0.

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), where a and b are the coefficients from the standard form of the quadratic function.

Front

What is the significance of the vertex in a parabola?

Back

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

Front

What does it mean for a quadratic function to be in vertex form?

Back

A quadratic function is in vertex form if it is expressed as f(x) = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.

Front

How can you determine if a quadratic function opens upwards or downwards?

Back

If the leading coefficient (a) is positive, the parabola opens upwards. If a is negative, the parabola opens downwards.

Front

What is the formula for the vertex of a parabola given in standard form?

Back

The vertex (h, k) can be found using h = -b/(2a) and k = f(h), where f(h) is the value of the function at x = h.