Question

Identify the quadratic function from the four functions

Answer 1

Quadratic Function is a function that takes the equation form of:

$\large \boxed{y = a {x}^{2} + bx + c}$

where a ≠ 0. However the form of Quadratic Function above can also be called "standard form" or general form because it is commonly used when defining the function. Quadratic Functions also have other two forms which are intercept form and vertex form.

Vertex Form

$\large \boxed{y = a {(x - h)}^{2} + k}$

Intercept Form

$\large \boxed{y = (ax - b)(bx - c)}$

The intercept form can be expressed as y = (x-a)(x-b) depending on the other perspective.

If you look at all four functions, you will notice that only two of functions have the second degree as highest degree while the third function has third degree as highest and fourth function has fourth degree. Recall the definition of Quadratic Function above that the highest degree of Quadratic Function can only be second degree (squared, x² as example). Therefore we can rule out the x³ and -2x⁴ away.

So our only quadratic functions are:

$\large{ \begin{cases}y = - {x}^{2} - 4 \\ y = {(x - 1)}^{2} - 7 \end{cases}}$

As for the f(x) = -x²-4. The equation is in standard form which is y = ax²+bx+c. The second equation is in vertex form which is y = a(x-h)²+k.

Answer

• The only quadratic functions are f(x) = -x²-4 and f(x) = (x-1)²-7
• -x²-4 is in standard form.
• (x-1)²-7 is in vertex form.

Hope this helps and let me know if you have any doubts.

Also let me know if you want me to convert the function into other form. For ex. convert the vertex form to standard form.

Happy Learning and Good Luck with your assignment!