Solving quadratic equations using square root

Front

What is the square root property in solving quadratic equations?

Back

The square root property states that if x^2 = a, then x = ±√a. This is used to find solutions of quadratic equations.

Front

How do you apply the square root property to the equation 2(x - 4)² = 200?

Back

First, divide both sides by 2 to get (x - 4)² = 100. Then, take the square root of both sides: x - 4 = ±10. Finally, solve for x: x = 14 or x = -6.

Front

What is the graph of a quadratic equation called?

Back

The graph of a quadratic equation is called a parabola.

Front

What are the solutions of the quadratic equation x² - 1 = 0?

Back

The solutions are x = 1 and x = -1.

Front

How do you solve the equation 5m² + 1 = 6 using square roots?

Back

First, isolate m²: 5m² = 5. Then, divide by 5: m² = 1. Finally, take the square root: m = ±1.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

How do you solve k² - 6 = 43 using square roots?

Back

First, isolate k²: k² = 49. Then, take the square root: k = ±7.

Front

What does it mean if a quadratic equation has no real solutions?

Back

It means that the discriminant (b² - 4ac) is less than zero, indicating that the parabola does not intersect the x-axis.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

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 formula x = -b/(2a).