Exercise 20 Page 557

To draw the graph of the given quadratic function written in standard form, we must start by identifying the values of a, b, and c. f(x)=x^2+4x-5 ⇔ f(x)= 1x^2+ 4x+( - 5) We can see that a= 1, b= 4, and c= - 5. Now, we will follow four steps to graph the function.

1. Find the axis of symmetry.
2. Calculate the vertex.
3. Identify the y-intercept and its reflection across the axis of symmetry.
4. Connect the points with a parabola.

   Finding the Axis of Symmetry

   The axis of symmetry is a vertical line with equation x= - b2 a. Since we already know the values of a and b, we can substitute them into the formula.

   x=- b/2a

   SubstituteII

   a= 1, b= 4

   x=- 4/2( 1)

   ▼

   Simplify right-hand side

   IdPropMult

   Identity Property of Multiplication

   x=- 4/2

   CalcQuot

   Calculate quotient

   x=- 2

   The axis of symmetry of the parabola is the vertical line with equation x=- 2.

   Calculating the Vertex

   To calculate the vertex, we can write the expression for the vertex by stating the x- and y-coordinates in terms of a and b. Vertex: ( - b/2 a, f(- b/2 a ) ) Note that the formula for the x-coordinate is the same as the formula for the axis of symmetry, which is x=- 2. Thus, the x-coordinate of the vertex is also - 2. To find the y-coordinate, we need to substitute - 2 for x in the given equation.

   f(x)=x^2+4x-5

   Substitute

   x= - 2

   f( - 2)=( - 2)^2+4( - 2)-5

   ▼

   Simplify right-hand side

   CalcPow

   Calculate power

   f(- 2)=4+4(- 2)-5

   Multiply

   Multiply

   f(- 2)=4-8-5

   AddSubTerms

   Add and subtract terms

   f(- 2)=- 9

   We found the y-coordinate, and now we know that the vertex is (- 2,- 9).

   Identifying the y-intercept and Its Reflection

   The y-intercept of the graph of a quadratic function written in standard form is given by the value of c. Thus, the point where our graph intercepts the y-axis is (0, - 5). Let's plot this point and its reflection across the axis of symmetry.

   

   Connecting the Points

   We can now draw the graph of the function. Since a= 1, which is positive, the parabola will open upwards. Let's connect the three points with a smooth curve.