PC Graphing Quadratics using Vertex Formula

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the point where the graph changes direction. It is the maximum or minimum point of the parabola.

Front

How do you find the vertex using the vertex formula?

Back

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

Front

Find the vertex of y = -5x^2 - 20x - 26.

Back

(-2, -6) using h = -(-20)/(2*-5) = -2 and k = f(-2) = -6.

Front

What is the axis of symmetry in a quadratic function?

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 = -b/(2a).

Front

Find the axis of symmetry for f(x) = x^2 - 8x + 15.

Back

x = 4, calculated using x = -(-8)/(2*1).

Front

What is the vertex of y = x^2 + 4x + 3?

Back

(-2, -1) using h = -4/(2*1) = -2 and k = f(-2) = -1.

Front

How do you determine if a quadratic opens upwards or downwards?

Back

If the coefficient 'a' in the quadratic equation y = ax^2 + bx + c is positive, the parabola opens upwards. If 'a' is negative, it opens downwards.

Front

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

Back

(-2, 16) using h = -(-4)/(2*-1) = -2 and k = f(-2) = 16.

Front

What is the vertex of y = -2x^2 + 4x + 3?

Back

(1, 5) using h = -4/(2*-2) = 1 and k = f(1) = 5.

Front

What does the vertex represent in a real-world context?

Back

In a real-world context, the vertex can represent the maximum or minimum value of a situation, such as the highest point of a projectile's path.