Quadratics Properties and Equations

Front

What is the equation for a parabola in factored form?

Back

The equation of a parabola in factored form is expressed as y = a(x - r1)(x - r2), where r1 and r2 are the roots or x-intercepts.

Front

What is the vertex form of a quadratic equation?

Back

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

Front

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

Back

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

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts (or roots) are the points where the graph of the quadratic function crosses the x-axis, found by solving the equation y = 0.

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = h, where h is the x-coordinate of the vertex.

Front

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

Back

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

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero, also known as the solutions of the equation.

Front

How can you determine if a quadratic equation has real roots?

Back

You can determine if a quadratic equation has real roots by calculating the discriminant (D = b² - 4ac). If D > 0, there are two real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

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.

Front

What is the significance of the vertex in a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on the direction it opens, and it represents the maximum or minimum value of the quadratic function.