Re-write the quadratic function below in Standard Form
y= 2(x - 2)2 – 7

Standard form:   y = 2x² - 8x + 1

Step-by-step explanation:

We are given the following quadratic function, y = 2(x - 2)² - 7, for which we must transform in its standard form.

The vertex form of a quadratic function is y = a(x - h)² + k (which is the format of the given equation).

⇒  If the value of "a" is positive, then the vertex is its minimum or lowest point on the graph.

⇒  If the value of "a" is negative, then the vertex is the maximum or highest point  on the graph.

The standard form of a quadratic function is y = ax² + bx + c, where a ≠ 0.

The first step in rewriting the given equation into its standard form  is expanding the binomial using the FOIL method, which transforms it into a perfect square trinomial.  

y = 2(x - 2)² - 7

       ⇒   (x - 2)(x - 2)

       ⇒   [ x² - 2x - 2x + 4 ]

y = 2(x - 2)² - 7

y = 2(x² - 2x - 2x + 4) - 7

y = 2(x² - 2x - 2x + 4) - 7

y = 2x² - 4x - 4x + 8 - 7

y = 2x² - 8x + 1.

Therefore, the quadratic function in standard form is y = 2x² - 8x + 1, where a = 2, b = -8, and c = 1.

Quadratic equations

Parabola

Quadratic functions

Vertex form

Functions

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