Question

determine the maximum or minimum of the quadratic function. express your answer in the form (x,y) and using decimals rounded to the hundredths.f(x)=2x^2+7-10

Answer 1

Exact Form:x=±√6/2

Decimal Form:x=1.22474487,−1.22474487

Explanation:

Answer 2

We are given the following quadratic equation

`f(x)=2x^2+7x-10`

The vertex is the maximum/minimum point of the quadratic equation.

The x-coordinate of the vertex is given by

`h=-(b)/(2a)`

Comparing the given equation with the general form of the quadratic equation, the coefficients are

a = 2

b = 7

c = -10

`h=-(b)/(2a)=-(7)/(2(2))=-(7)/(4)=-1.75`

The y-coordinate of the vertex is given by

`\begin{gathered} f(x)=2x^2+7x-10 \\ f(-1.75)=2(-1.75)^2+7(-1.75)-10 \\ f(-1.75)=2(3.0625)^{}-12.25-10 \\ f(-1.75)=6.125^{}-12.25-10 \\ f\mleft(-1.75\mright)=-16.13 \end{gathered}`

This means that we have a minimum point.

Therefore, the minimum point of the given quadratic equation is

`(-1.75,-16.13)`