Example #3

Graph y = -2x2 + 3x + 5

Step 1: Find the axis of symmetry.

x = -b/2a

x = -3/2(-2)

x = -3/-4

x = 3/4

Axis of Symmetry : x = 3/4

Step 2: Find the vertex.

We know from Step 1 that x = 3/4

y = -2x2 + 3x + 5

Plug 3/4 into the equation to solve for y.

y = -2(3/4_^2 + 3(3/4) + 5 Evaluate the exponents first.

y = -2(9/16) +3(3/4)+5 Evaluate the multiplication next

y = -9/8 + 9/4 + 5 Add by getting a common denominator

y = -9/8 + 18/8 + 40/8

y = 49/8

Vertex: (3/4) , (49/8)

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

0 = -2x2 + 3x + 5
To solve, factor the equation. Since a is negative, factor out the negative 1.

0 = -1(2x2 + 3x + 5)

Find the factors of a times c that add to equal b.

The factors of -10 that add to equal -3 are -5 and 2.

0 = -1(x - 5/2)(x + 2/2) Remember, to divide by a and reduce.

0 = -1(x - 5/2)(x+1) Since we are solving, we do not have to move the 2  to the front of the factor.

-1 ≠ 0 or x - 5/2 = 0 or x + 1 = 0

x = 5/2 ; x = -1

x-intercepts: ( 5/2, 0) and (-1, 0)

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

c = 5

The y-intercept is (0,5)

Graph y = -2x2 + 3x + 5

We will now graph everything that we have found.

Axis of Symmetry : x = 3/4

Vertex: (3/4) , (49/8)

x-intercepts: ( 5/2, 0) and (-1, 0)

The y-intercept is (0,5)

Now, draw a quadratic curve connecting the points.

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