Mar 2025 -Solve Quadratic Equations - Formula,Factors, & Zeros

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 ax² + bx + c = 0.

Front

Solve using the quadratic formula: 9x² = 4 + 7x

Back

Rearranging gives 9x² - 7x - 4 = 0. Using the quadratic formula, x = (7 ± √(7² - 4*9*(-4))) / (2*9). Solutions are x = 1 and x = -0.5.

Front

Why are quadratic equations set equal to zero?

Back

Because we are trying to find the x-intercepts and that happens when y=0.

Front

Solutions of a quadratic equation are also called:

Back

All of the above (roots, x-intercepts, zeros).

Front

What are the zeros of this graph? If the graph intersects the x-axis at (-4, 0) and (2, 0)

Back

x = {-4, 2}.

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.

Front

What does the discriminant (b² - 4ac) tell us?

Back

The discriminant determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, found at x = -b/(2a).

Front

How do you find the axis of symmetry for a quadratic equation?

Back

The axis of symmetry is given by the formula x = -b/(2a).

Front

What is the standard form of a quadratic equation?

Back

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