Question

Two quadratic functions are shown.
Function 1:
f(x) = 2x2 - 8x + 1
Function 2:
x g(x)
-2 2
-1 -3
0 2
1 17

Which function has the least minimum value and what are its coordinates? (5 points)

Function 1 has the least minimum value and its coordinates are (0, 1).
Function 1 has the least minimum value and its coordinates are (2, -7).
Function 2 has the least minimum value and its coordinates are (0, 2).
Function 2 has the least minimum value and its coordinates are (-1, -3).
​

Answer 1

Answer:

Function 1 has the least minimum value and its coordinates are (2, -7).

Step-by-step explanation:

Two quadratic functions are shown.

Function 1:

$f(x) = 2x^2 - 8x + 1$

Function 2:

x        g(x)

-2         2

-1         -3

0         2

1         17

LEts find the vertex to get the minimum value

to get the minimum value for function 1 we use formula $x=\frac{-b}{2a}$

$f(x) = 2x^2 - 8x + 1$, a=2, b=-8

$x=\frac{-b}{2a}=\frac{8}{2(2)}=2$

when x=2, the value of $f(2) = 2(2)^2 - 8(2) + 1=-7$

minimum point of function 1 is (2,-7)

For function 2, we find the minimum point using the table

minimum point of function 2 is (-1,-3)

Function 1 has the least minimum -7.

Function 1 has the least minimum value and its coordinates are (2, -7).

Answer 2

The true statement is (b) function 1 has the least minimum value and its coordinates are (2, -7).

The first quadratic function is given as:

• $f(x)= 2x^2 - 8x +1$

Factor out 2 in the above equation

$f(x)= 2(x^2 - 4x) +1$

Rewrite the expression in the bracket, as follows:

$f(x)= 2(x^2 - 4x + 4 - 4) +1$

This gives

$f(x)= 2(x^2 - 4x + 4 ) -8+1$

$f(x)= 2(x^2 - 4x + 4 ) -7$

Express x^2 - 4x + 4 as a perfect square

$f(x)= 2(x - 2)^2 -7$

A quadratic function is represented as:

$f(x)= a(x - h)^2 +k$

Where

$Vertex = (h,k)$

By comparison, we have:

• $Vertex = (2,-7)$ --- this represents the minimum of function 1

From the graph, the minimum of function 2 is:

• $Vertex = (-1,-3)$

(2,-7) is lesser than (-1,-3).

Hence, the function 1 has the least minimum value at a coordinate of (2,-7)

Read more about quadratic functions at:

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