Quadratics Homework

Front

What is the vertex form of a quadratic equation?

Back

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

Front

How do you convert a quadratic equation from standard form to vertex form?

Back

To convert from standard form (f(x) = ax² + bx + c) to vertex form, complete the square.

Front

What is the vertex of the parabola given by the equation y = 2(x - 3)² + 5?

Back

The vertex is (3, 5).

Front

What does the 'a' value in the vertex form of a quadratic indicate?

Back

The 'a' value indicates the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola.

Front

What is the axis of symmetry for the parabola given by the equation y = (x + 4)² - 7?

Back

The axis of symmetry is x = -4.

Front

How can you determine if a parabola opens upwards or downwards?

Back

If the 'a' value in the vertex form is positive, the parabola opens upwards; if negative, it opens downwards.

Front

What is the maximum or minimum value of the function y = -3(x + 2)² + 4?

Back

The maximum value is 4.

Front

What is the standard form of the quadratic equation y = (x - 1)² + 2?

Back

The standard form is y = x² - 2x + 1 + 2, which simplifies to y = x² - 2x + 3.

Front

How do you find the y-intercept of a quadratic function?

Back

To find the y-intercept, set x = 0 in the quadratic equation and solve for y.

Front

What is the y-intercept of the equation y = 2x² + 3x - 5?

Back

The y-intercept is -5.