Quadratics Unit 1/2 way point

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is given by y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you convert from vertex form to standard form?

Back

To convert from vertex form y = a(x - h)² + k to standard form y = ax² + bx + c, expand the equation: y = a(x² - 2hx + h²) + k.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts of a quadratic function are the points where the graph intersects the x-axis, found by setting y = 0 and solving the equation.

Front

What is intercept form of a quadratic equation?

Back

The intercept form of a quadratic equation is given by y = a(x - p)(x - q), where p and q are the x-intercepts.

Front

How can you find the x-intercepts from the intercept form?

Back

To find the x-intercepts from the intercept form y = a(x - p)(x - q), set y = 0 and solve for x: 0 = a(x - p)(x - q).

Front

What is the general (standard) form of a quadratic equation?

Back

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

Front

How do you write a quadratic equation from a graph?

Back

To write a quadratic equation from a graph, identify the vertex and x-intercepts, then use the vertex form or intercept form to construct the equation.

Front

What is the relationship between factored form and graphing quadratics?

Back

Factored form y = a(x - p)(x - q) shows the x-intercepts directly, which can be plotted to graph the quadratic.

Front

What is the box method for multiplying polynomials?

Back

The box method involves drawing a box divided into sections, where each section represents the product of terms from the polynomials being multiplied.

Front

How do you multiply (x + 2)(x + 3) using the box method?

Back

Draw a 2x2 box. Label the rows with (x + 2) and the columns with (x + 3). Fill in the boxes: x², 3x, 2x, 6. Combine like terms: x² + 5x + 6.