Writing Quadratic Equations

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 and a ≠ 0.

Front

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

Back

To convert from vertex form y = a(x - h)² + k to standard form, expand the equation: y = a(x² - 2hx + h²) + k, then simplify to y = ax² + bx + c.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts of a quadratic function are the points where the graph intersects the x-axis, found by solving the equation y = 0.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

How can you find the vertex from the standard form of a quadratic equation?

Back

The vertex (h, k) can be found using the formula h = -b/(2a) and then substituting h back into the equation to find k.

Front

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

Back

The 'a' value determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

What are the factors of a quadratic equation?

Back

Factors of a quadratic equation are the expressions that can be multiplied to give the quadratic equation, typically in the form (x - r)(x - s) where r and s are 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 is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, b² - 4ac, which determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

How do you determine if a quadratic equation has real solutions?

Back

To determine if a quadratic equation has real solutions, calculate the discriminant (b² - 4ac). If it is non-negative, the equation has real solutions.