Quadratics- Factored Form

Front

What is the vertex of a quadratic function in standard form?

Back

The vertex is the point where the graph of the quadratic function reaches its maximum or minimum value, given by the coordinates (h, k) in the vertex form y = a(x - h)² + k.

Front

What are the zeros of a quadratic function?

Back

The zeros (or x-intercepts) are the values of x for which the quadratic function equals zero. They can be found by factoring the quadratic equation or using the quadratic formula.

Front

How do you find the vertex of a quadratic function given in factored form?

Back

To find the vertex from the factored form y = a(x - r)(x - s), calculate the x-coordinate as (r + s)/2 and substitute it back into the equation to find the y-coordinate.

Front

What is the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is expressed as y = a(x - r)(x - s), where r and s are the roots of the equation.

Front

How many solutions can a quadratic equation have?

Back

A quadratic equation can have two solutions, one solution, or no real solutions, depending on the discriminant (b² - 4ac) of the equation.

Front

What does it mean if a quadratic graph touches the x-axis at one point?

Back

If a quadratic graph touches the x-axis at one point, it means the equation has one real solution (a repeated root), and the vertex of the parabola is on the x-axis.

Front

What is the significance of the coefficient 'a' in the quadratic equation?

Back

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

Front

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

Back

To convert from standard form (ax² + bx + c) to factored form, you can factor the quadratic expression or use the quadratic formula to find the roots.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What are the x-intercepts of the quadratic function y = x² - 8x - 48?

Back

The x-intercepts are the solutions to the equation x² - 8x - 48 = 0, which can be found by factoring or using the quadratic formula.