Exercise 39 Page 550

Consider the general expression of a quadratic function, y=ax^2+ bx+ c, where a ≠ 0. Let's note three things we can learn from this equation.

The y-intercept is c.
The equation of the axis of symmetry is x=- b2a.
The x-coordinate of the vertex is - b2a.

We will start by identifying the values of a, b, and c. y=7x^2-28x+14 ⇕ y=7x^2+( - 28)x+ 14We can see that a = 7, b = - 28, and c = 14. Since the y-intercept is given by the value of c, we know that the y-intercept is 14. Let's now substitute a=7 and b=- 28 into - b2a to find the axis of symmetry.

x = - b/2a

SubstituteII

a= 7, b= - 28

x = - - 28/2(7)

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Simplify

Multiply

x = - - 28/14

RemoveNegFracAndNum

- - a/b= a/b

x = 28/14

CalcQuot

Calculate quotient

x = 2

The equation of the axis of symmetry is x=2.
To find the vertex of the parabola, we will need to think of y as a function of x, y=f(x). We can write the expression for the vertex by stating the x- and y-coordinates in terms of a and b. Vertex: ( - b/2a, f(- b/2a ) ) When determining the axis of symmetry, we found that - b2a=2. Therefore, the x-coordinate of the vertex is 2 and the y-coordinate is f(2). To find this value, substitute our x-coordinate for x in the given equation.

f(x)=7x^2-28x+14

Substitute

x= 2

f( 2)=7( 2)^2-28( 2)+14

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Simplify right-hand side

CalcPow

Calculate power

f(2)=7(4)-28(2)+14

MultNegPos

(- a)b = - ab

f(2)=7(4)-56+14