Solving Quadratic equations and nonlinear systems

Front

What must be true when using factoring to solve a quadratic equation?

Back

The equation must be set equal to 0.

Front

What is the quadratic formula used for?

Back

To find the solutions of a quadratic equation in the form ax² + bx + c = 0.

Front

If the graph of a quadratic does not intercept the x-axis, how many real solutions does it have?

Back

No Real Solution.

Front

What are the x-intercepts of a quadratic function?

Back

The points where the graph intersects the x-axis, found by setting y = 0.

Front

Identify the values of a, b, and c in the quadratic equation: 4x² = 8x + 3.

Back

a = 4, b = -8, c = -3.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0.

Front

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

Back

It indicates the nature of the roots: if > 0, two real solutions; if = 0, one real solution; if < 0, no real solutions.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula (-b/2a, f(-b/2a)).

Front

What is the axis of symmetry in a quadratic function?

Back

The vertical line that divides the parabola into two mirror images, given by x = -b/2a.

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.