graph the quadratic function f(x)=-2x^2-x-2.

Question

graph the quadratic function.

Answer 1

Given equation f(x) = -2x^2-x-2

y = -2x^2-x-2

If x = -1,0,1 then set of coordinate pair would be y = -3,.-2 -5.

Graph

Draw the coordinate plane.

Plot the above points.

Connect the plotted points Neatly like a curve.

Then the formed parabola indicating given quadratic equation.

Answer 2

Note :

To graph a quadratic function follow the steps :

Step 1 : Find the equation of the axis of symmetry.

Step 2 : Find vertex, and determine wheather it is a maximum or minimum.

Step 3 : Find the y - intercept.

Step 4 : Use symmetry to find additional points on the graph, if necessary.

Step 5 : Connect the points with a smooth curve.

The function is f(x) = y = - 2x² - x - 2.

The standard form of quadratic function is f(x) = ax² + bx + c.

Step 1 :

Find the axis of symmetry :

Formula for the equation of the axis of symmetry:  x = - b/2a.

Substitute the values of b = - 1 and a = - 2 in the formula, x = - b/2a.

x = - (- 1)/2(- 2)

x = - 1/4.

The equation for the axis of symmetry is x = - 1/4.

Step 2 :

Find the vertex :

To find the vertex, use the value of equation for the axis of symmetry as the  x - coordinate of the vertex.

To find the y - coordinate, substitute the value of x = - 1/4 in the original function, y = - 2x² - x - 2.

y = - 2(- 1/4)² - (- 1/4) - 2

y = - 2(1/16) + 1/4 - 2

y = - 15/8.

The vertex is (- 1/4, - 15/8).

Determine whether the function has maximum or minimum value :

The value of a = - 2 < 0 (negative), so the graph of function opens downward and has a maximum value.

The maximum value (y - coordinate of the vertex) is - 15/8.

Step 3 :

Find the y -  intercept :

To find the y - intercept, Substitute the value x = 0 in the original function, f(x) = y = - 2x² - x - 2.

y = - 2(0)² - 0 - 2

y = - 2.

The y - intercept is - 2.

Step 4 :

• Lets find the another point.Choose an x - value of 1/2 and substitute.The new point is at (1/2, - 3).
• The point paired with it on other side of the axis of symmetry is (- 1, -3) and has the same y - value.
• Since, The axis of symmetry devides the parabola into two equal parts.So, if thereis a point (1/2, - 3) on one side, there is a corresponding point on other side that is the same distance from the axis of symmetry and has the same y - value.
• The distance between the points (1/2, - 3) and (- 1/4, -3) = 3/4 = The distance between (- 1/4, - 3) and the point paired with it on other side of the axis of symmetry and has the same y - value.
• The distance between (- 1/4, - 3) and the point paired with it on other side of the axis of symmetry. = - 1/4 - 3/4 = - 4/4 = - 1.
• Therefore, The point paired with it on other side of the axis of symmetry is (- 1, -3).
• Repeate this, and choose an x - value of 1 and substitute.The new point is at (1, - 5).and its correspondin point is (- 3/2, - 5).
   
• Connect these points and create a smooth curve.

Graph :