MASTER How to write the equation of a parabola in vertex and standard form given the vertex and thro

The video tutorial explains how to write the equation of a parabola in both vertex and standard forms. It begins by defining the vertex form as y = a * (X - H)^2 + K and the standard form as y = a * X^2 + BX + C. The tutorial then demonstrates how to use given vertex and point coordinates to solve for 'a' and write the equation in vertex form. It also covers converting the vertex form to standard form through expansion and the FOIL method. Several example problems are provided to illustrate the process, concluding with a final example and summary.

What is the vertex form of a parabola?

• y = a(x - k)^2 + h

• y = a * (x - h)^2 + k

• y = ax^2 + c

• y = ax^2 + bx + c

In the vertex form equation y = a * (x - h)^2 + k, what do h and k represent?

• The x-intercepts

• The y-intercept

• The vertex of the parabola

• The coefficients of x

What is the first step in writing the equation of a parabola given a vertex and a point?

• Find the y-intercept

• Convert to standard form

• Calculate the axis of symmetry

• Plug the vertex and point into the vertex form equation

How do you convert a vertex form equation to standard form?

• By factoring

• By using the quadratic formula

• By expanding and simplifying

• By completing the square

When expanding (x + 4)^2, what is the resulting expression?

• x^2 + 4x + 4

• x^2 + 4

• x^2 + 16

• x^2 + 8x + 16

In the equation y = -3(x - 5)^2, what does the -3 represent?

• The direction and width of the parabola

• The axis of symmetry

• The y-intercept

• The vertex

What is the standard form of the equation y = 1/3(x + 1)^2 - 4?

• y = x^2 + 2x - 4

• y = 1/3x^2 + 2/3x - 11/3

• y = x^2 + 1/3x - 11/3

• y = 1/3x^2 + x - 4