I need to find the intercepts of the graph of the parabola.

Question

y = x^2 + 5x +4
I have to have 2 x-intercepts and 1 y-intercept
thanks.

Answer 1

Given parabola y = x ^2 + 5x + 4

To find x  intercept substitute y  = 0 in above equation.

x ^2 + 5x + 4 = 0

x ^2 + 4x + x + 4 = 0

x (x + 4) + 1(x + 4) = 0

Take out common factors.

(x + 4)(x + 1) = 0

x + 4 = 0

Subtract 4 from each side.

x  = -4

And x + 1 = 0

Subtract 1 from each side.

x  = -1

x  intercepts of parabola is -1 and -4.

To find y  intercept substitute x  = 0 in parabola equation.

y  = (0)^2 + 5(0) + 4

y  = 0 + 0 + 4

y  = 4.

To find vertex of parabola

y  = x ^2 + 5x + 4

Compare it to standard equation of parabola y  = ax ^2 + bx + c.

a  = 1 , b  = 5, c  = 4.

Axis of symmetry x = -b /2a.

x  = -5/2 = -2.5

Substitute x  value in y  = x ^2 + 5x + 4.

y  = 6.25 -12.5 + 4

y  = -2.25

Vertex of parabola is ( x , y ) = (-2.5 , -2.25).

x  intercepts are ( -4 , 0 ) and ( -1 , 0 ).

y  intercepts are ( 0 , 4 ).

Graph :

Draw the coordinate plane.

Plot the above points.

Connect the plotted points neatly.

Then formed curve is indicating y  = x ^2 + 5x +4.

From the graph we can observe x  intercepts are ( -4 , 0 ) and ( -1 , 0 ).

y  intercepts are ( 0 , 4 ).

Answer 2

Parabola equation is y = x ^2 + 5x + 4

To find x intercept substitute y  = 0 in above equation.

x ^2 + 5x + 4 = 0

x ^2 + 4x + x + 4 = 0

x (x + 4) + 1(x + 4) = 0

(x + 4)(x + 1) = 0

x + 4 = 0  ----> x = - 4

x + 1 = 0 -------> x = - 1

 

x  intercepts of parabola is -1 and -4.

To find y intercept substitute x  = 0 in parabola equation.

y  = (0)^2 + 5(0) + 4

y  = 4.

 

To find vertex of parabola y  = x ^2 + 5x + 4

Compare it to standard parabola  equation y  = ax ^2 + bx + c.

a  = 1, b  = 5, c  = 4.

Axis of symmetry x = -b /2a.

x  = -5/2 = -2.5

Substitute x value in y  = x ^2 + 5x + 4.

y  = 6.25 -12.5 + 4 = -2.25

 

Vertex of parabola is ( x , y ) = (-2.5 , -2.25).

x  intercepts are ( -4 , 0 ) and ( -1 , 0 ).

y  intercepts is ( 0 , 4 ).

Graph :

Draw the coordinate plane, and plot the points.

Draw a curve through the points torepresent y = x ^2 + 5x +4.

Comments

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