SOLUTION: Complete the follwing function for g(x)=-4x^2+16x+19 Generate the graph and find the Vertex and x&y intercepts for the graph, show all work

Algebra ->  Graphs -> SOLUTION: Complete the follwing function for g(x)=-4x^2+16x+19 Generate the graph and find the Vertex and x&y intercepts for the graph, show all work       Log On


   



Question 56536: Complete the follwing function for g(x)=-4x^2+16x+19 Generate the graph and find the Vertex and x&y intercepts for the graph, show all work
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
I think you forgot an x, so I plugged it in.
Complete the follwing function for g%28x%29=-4x%5E2%2B16x%2B19 Generate the graph and find the Vertex and x&y intercepts for the graph, show all work.
Your quadratic equation is in standard form:highlight%28f%28x%29=ax%5E2%2Bbx%2Bc%29. Your a=-4, b=16, c=19 (note: a is negative, so your parabola opens down.)
First find the axis of symmetry, which is also the x value of the vertex using the formula highlight%28x=-b%2F2a%29
x=-%2816%2F%282%28-4%29%29%29
x=-16%2F-8
x=2 This is your axis of symmetry and x value of the vertex, to find the y value of the vertex find g(2):
g%282%29=-4%282%29%5E2%2B16%282%29%2B19
g%282%29=-4%284%29%2B16%282%29%2B19
g%282%29=-16%2B32%2B19
g%282%29=35
Your vertex is (2,35). Plot that point.
The y-intercept is found by letting x =0 and solve for y:
g%280%29=-4%280%29%5E2%2B16%280%29%2B19
g%280%29=19
The y-intercept is (0,-19).
The x-intercept is found by letting g(x)=0 and solving for x:
0=-4x%5E2%2B16x%2B19
This can't be factored, so use the quadratic formula to solve it:
highlight%28x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29%29
x=%28-%2816%29%2B-sqrt%28%2816%29%5E2-4%28-4%29%2819%29%29%29%2F%282%28-4%29%29
x=%28-16%2B-sqrt%28256%2B304%29%29%2F-8
x=%28-16%2B-sqrt%28560%29%29%2F-8
x=%28-16%2B-sqrt%2816%29%2Asqrt%2835%29%29%2F-8
x=%28-16%2B-4%2Asqrt%2835%29%29%2F-8
x=%28-16-4%2Asqrt%2835%29%29%2F-8 and x=%28-16%2B4%2Asqrt%2835%29%29%2F-8
x=-4%284%2Bsqrt%2835%29%29%2F%28-4%2A2%29 and x=-4%284-sqrt%2835%29%29%2F%28-4%2A2%29
x=%284%2Bsqrt%2835%29%29%2F2 and x=%284-sqrt%2835%29%29%2F2
x~~4.958039892 and x~~-.9580398915
The program is not responding to my attempts to regraph this.
Plot the vertex(2,35), the y-int (0,19), the x-int (-.95,0) and (4.95,0) and connect the dots. You should have an upside down parabola.
Happy Calculating!!!