Writing Quadratics Given Vertex and a Point

Front

What is the vertex form of a quadratic equation?

Back

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

Front

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

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola (larger |a| means narrower, smaller |a| means wider).

Front

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

Back

To find the vertex from standard form y = ax² + bx + c, use the formula h = -b/(2a) and k = f(h).

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that passes through the vertex of the parabola, given by the equation x = h.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.

Front

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

Back

If the 'a' value in the vertex form y = a(x - h)² + k is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What are the roots of a quadratic equation?

Back

The roots (or zeros) are the x-values where the quadratic function intersects the x-axis, found by solving the equation y = 0.

Front

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

Back

The y-intercept can be found by evaluating the function at x = 0, i.e., y = a(0 - h)² + k.

Front

What is the relationship between the vertex and the axis of symmetry?

Back

The vertex lies on the axis of symmetry, which divides the parabola into two mirror-image halves.

Front

How do you write a quadratic equation in vertex form given a vertex and a point?

Back

Use the vertex form y = a(x - h)² + k, substitute the vertex (h, k), and use the given point to solve for 'a'.