3.06 Graphing Quadratic Functions in Standard Form

Guided Practice #1

Graph y = 3x² - 5x - 2

Step 1) Find the axis of symmetry.

x = [-b]/[2a]

x = [-()]/[2()]

x = 5/6

Step 2) Find the vertex. We know from the first step that x = 5/6

Plug x = 5/6 into the equation y = 3x² - 5x - 2 to solve for y.

y = 3(5/6)squared - 5(5/6) - 2

Evaluate the exponents first.

y = 3(25/36) - 5(5/6) - 2

Evaluate the multiplication next.

y = 25/12 - 25/6 - 2

Add by getting a common denominator.

y = 25/12 - 50/12 - 24/12

Subtract.

y = -49/12

The vertex is (5/6, -49/12) .

Step 3) Find the x-intercepts. Set y equal to 0 and solve.

0 = 3x² - 5x - 2

To solve, factor the equation. Find the factors of a times c that add to equal b.

The factors of -6 that add to equal -5 are -6 and 1.

Remember to divide by a and reduce.

0 = (x - ()/3)(x + ()/3)

0 = (x - 2)(x +1/3)

x -2 = 0 or x + = 0

x =

Axis of Symmetry: x = 5/6

Vertex: (5/6, -49/12)

x-intercepts: (, 0) and (2, 0)

Step 4) Find the y-intercept. The y-intercept is the c value.

c =

The y-intercept is (0, -2).

Now, draw a quadratic curve connecting the points.