Test: Identifying Quadratic Forms and parts

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 is the Standard Form of a quadratic equation?

Back

The Standard Form of a quadratic equation is given by y = ax² + bx + c, where a, b, and c are constants.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts (or zeros) of a quadratic function are the points where the graph intersects the x-axis, found by setting y = 0.

Front

How do you find the x-intercepts from factored form?

Back

To find the x-intercepts from factored form y = a(x-p)(x-q), set y = 0 and solve for x, giving x = p and x = q.

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 convert from Vertex Form to Standard Form?

Back

To convert from Vertex Form y = a(x-h)² + k to Standard Form, expand the equation and simplify to the form y = ax² + bx + c.

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, given by the equation x = h in Vertex Form.

Front

What does the 'a' value in a quadratic equation indicate?

Back

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

Front

How do you find the vertex from Standard Form?

Back

To find the vertex from Standard Form y = ax² + bx + c, use the formula h = -b/(2a) and then substitute h back into the equation to find k.

Front

What is the relationship between the roots and the vertex of a quadratic function?

Back

The vertex lies on the axis of symmetry, which is equidistant from the roots (x-intercepts) of the quadratic function.