Parabola Equations (Period 7)

Front

What is a parabola?

Back

A parabola is a symmetrical, U-shaped curve that represents the graph of a quadratic function. It can open upwards or downwards depending on the coefficient of the squared term.

Front

What is the standard form of a quadratic equation?

Back

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

Front

What does the coefficient 'a' in a quadratic equation determine?

Back

The coefficient 'a' determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards. A larger absolute value of 'a' makes the parabola narrower.

Front

How do you find the vertex of a parabola in standard form?

Back

The vertex (h, k) of a parabola in standard form y = ax² + bx + c can be found using the formula h = -b/(2a) and k = f(h).

Front

What is the vertex of the parabola given by y = 2(x - 3)² + 4?

Back

The vertex is (3, 4).

Front

What is the axis of symmetry of a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula x = h, where (h, k) is the vertex.

Front

How do you determine the roots of a quadratic function?

Back

The roots of a quadratic function can be found by factoring, using the quadratic formula, or by completing the square. They are the x-values where the function equals zero.

Front

What are the roots of the function f(x) = (x - 1)(x + 2)?

Back

The roots are x = 1 and x = -2.

Front

What is the significance of the y-intercept in a parabola?

Back

The y-intercept is the point where the parabola crosses the y-axis. It can be found by evaluating the function at x = 0.

Front

How do you find the y-intercept of the function y = 3x² - 5x + 2?

Back

The y-intercept is found by substituting x = 0: y = 3(0)² - 5(0) + 2 = 2. So, the y-intercept is (0, 2).