Solving Quadratics Review

Front

What is the formula to find the x-value of the vertex in a quadratic equation in standard form?

Back

x = -\frac{b}{2a}

Front

How can you determine if a parabola opens upwards or downwards from its equation?

Back

The sign of the coefficient 'a' in the quadratic equation determines the direction of the parabola's opening.

Front

What is the first step in solving a quadratic equation using the square root method?

Back

Isolate the x² term on one side of the equation.

Front

What are the solutions to the equation 3x² - 9 = 3?

Back

x = 2 or x = -2

Front

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

Back

It means the parabola does not intersect the x-axis.

Front

How do you solve the equation x² + 12 = 5?

Back

Rearrange to x² = -7, which has no real solutions.

Front

What is the general form of a quadratic equation?

Back

The general form is ax² + bx + c = 0.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: two real solutions, one real solution, or no real solutions.

Front

How do you find the y-value of the vertex of a parabola?

Back

Substitute the x-value of the vertex into the original quadratic equation.

Front

What is the vertex form of a quadratic equation?

Back

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