Solving Quadratics by using the Quadratic Formula

Front

What is the standard form for a Quadratic?

Back

ax² + bx + c

Front

If b²-4ac is positive, the quadratic equation has:

Back

Two real solutions that are different

Front

Solve Using the Quadratic Formula: x² + 4x - 40 = -8

Back

x = -8 and x = 4

Front

In the equation y = x² + 5x + 7, identify the coefficients: a, b, c.

Back

a=1, b=5, c=7

Front

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

Back

x = 1.16 and x = -0.38

Front

What does the discriminant (b² - 4ac) tell us about the solutions of a quadratic equation?

Back

It indicates the nature of the roots: positive means two real solutions, zero means one real solution, negative means two imaginary solutions.

Front

What is the Quadratic Formula?

Back

x = (-b ± √(b² - 4ac)) / (2a)

Front

What is the vertex form of a quadratic equation?

Back

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

Front

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

Back

x = -b / (2a)

Front

What is the significance of the leading coefficient in a quadratic equation?

Back

It determines the direction of the parabola: if positive, it opens upwards; if negative, it opens downwards.