Solving Quadratic Equations

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What are the x-intercepts of a quadratic equation?

Back

The x-intercepts (or roots) of a quadratic equation are the points where the graph intersects the x-axis, corresponding to the solutions of the equation.

Front

How can you determine the number of solutions a quadratic equation has?

Back

The number of solutions can be determined using the discriminant (D = b² - 4ac). If D > 0, there are 2 solutions; D = 0 means 1 solution; D < 0 indicates no real solutions.

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 do you find the vertex of the parabola given in vertex form y = a(x-h)² + k?

Back

The vertex is the point (h, k).

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 = -b/(2a).

Front

What does it mean for a quadratic equation to have no real solutions?

Back

It means that the graph of the quadratic does not intersect the x-axis, which occurs when the discriminant is negative.

Front

What is the factored form of a quadratic equation?

Back

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

Front

How do you convert from factored form to standard form?

Back

Expand the factored form using the distributive property to obtain the standard form ax² + bx + c.

Front

What is the quadratic formula?

Back

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