Graph j(x)=2x^2-5x+4

Math
j(x)=2×2-5x+4
Find the properties of the given parabola.
Tap for more steps…
Rewrite the equation in vertex form.
Tap for more steps…
Complete the square for 2×2-5x+4.
Tap for more steps…
Use the form ax2+bx+c, to find the values of a, b, and c.
a=2,b=-5,c=4
Consider the vertex form of a parabola.
a(x+d)2+e
Substitute the values of a and b into the formula d=b2a.
d=-52(2)
Multiply 2 by 2.
d=-54
Find the value of e using the formula e=c-b24a.
Tap for more steps…
Simplify each term.
Tap for more steps…
Raise -5 to the power of 2.
e=4-254⋅2
Multiply 4 by 2.
e=4-258
e=4-258
To write 4 as a fraction with a common denominator, multiply by 88.
e=4⋅88-258
Combine 4 and 88.
e=4⋅88-258
Combine the numerators over the common denominator.
e=4⋅8-258
Simplify the numerator.
Tap for more steps…
Multiply 4 by 8.
e=32-258
Subtract 25 from 32.
e=78
e=78
e=78
Substitute the values of a, d, and e into the vertex form a(x+d)2+e.
2(x-54)2+78
2(x-54)2+78
Set y equal to the new right side.
y=2(x-54)2+78
y=2(x-54)2+78
Use the vertex form, y=a(x-h)2+k, to determine the values of a, h, and k.
a=2
h=54
k=78
Since the value of a is positive, the parabola opens up.
Opens Up
Find the vertex (h,k).
(54,78)
Find p, the distance from the vertex to the focus.
Tap for more steps…
Find the distance from the vertex to a focus of the parabola by using the following formula.
14a
Substitute the value of a into the formula.
14⋅2
Multiply 4 by 2.
18
18
Find the focus.
Tap for more steps…
The focus of a parabola can be found by adding p to the y-coordinate k if the parabola opens up or down.
(h,k+p)
Substitute the known values of h, p, and k into the formula and simplify.
(54,1)
(54,1)
Find the axis of symmetry by finding the line that passes through the vertex and the focus.
x=54
Find the directrix.
Tap for more steps…
The directrix of a parabola is the horizontal line found by subtracting p from the y-coordinate k of the vertex if the parabola opens up or down.
y=k-p
Substitute the known values of p and k into the formula and simplify.
y=34
y=34
Use the properties of the parabola to analyze and graph the parabola.
Direction: Opens Up
Vertex: (54,78)
Focus: (54,1)
Axis of Symmetry: x=54
Directrix: y=34
Direction: Opens Up
Vertex: (54,78)
Focus: (54,1)
Axis of Symmetry: x=54
Directrix: y=34
Select a few x values, and plug them into the equation to find the corresponding y values. The x values should be selected around the vertex.
Tap for more steps…
Replace the variable x with 0 in the expression.
f(0)=2(0)2-5⋅0+4
Simplify the result.
Tap for more steps…
Simplify each term.
Tap for more steps…
Raising 0 to any positive power yields 0.
f(0)=2⋅0-5⋅0+4
Multiply 2 by 0.
f(0)=0-5⋅0+4
Multiply -5 by 0.
f(0)=0+0+4
f(0)=0+0+4
Simplify by adding zeros.
Tap for more steps…
Add 0 and 0.
f(0)=0+4
Add 0 and 4.
f(0)=4
f(0)=4
The final answer is 4.
4
4
The y value at x=0 is 4.
y=4
Replace the variable x with -1 in the expression.
f(-1)=2(-1)2-5⋅-1+4
Simplify the result.
Tap for more steps…
Simplify each term.
Tap for more steps…
Raise -1 to the power of 2.
f(-1)=2⋅1-5⋅-1+4
Multiply 2 by 1.
f(-1)=2-5⋅-1+4
Multiply -5 by -1.
f(-1)=2+5+4
f(-1)=2+5+4
Simplify by adding numbers.
Tap for more steps…
Add 2 and 5.
f(-1)=7+4
Add 7 and 4.
f(-1)=11
f(-1)=11
The final answer is 11.
11
11
The y value at x=-1 is 11.
y=11
Replace the variable x with 2 in the expression.
f(2)=2(2)2-5⋅2+4
Simplify the result.
Tap for more steps…
Simplify each term.
Tap for more steps…
Multiply 2 by (2)2 by adding the exponents.
Tap for more steps…
Multiply 2 by (2)2.
Tap for more steps…
Raise 2 to the power of 1.
f(2)=2(2)2-5⋅2+4
Use the power rule aman=am+n to combine exponents.
f(2)=21+2-5⋅2+4
f(2)=21+2-5⋅2+4
Add 1 and 2.
f(2)=23-5⋅2+4
f(2)=23-5⋅2+4
Raise 2 to the power of 3.
f(2)=8-5⋅2+4
Multiply -5 by 2.
f(2)=8-10+4
f(2)=8-10+4
Simplify by adding and subtracting.
Tap for more steps…
Subtract 10 from 8.
f(2)=-2+4
Add -2 and 4.
f(2)=2
f(2)=2
The final answer is 2.
2
2
The y value at x=2 is 2.
y=2
Replace the variable x with 3 in the expression.
f(3)=2(3)2-5⋅3+4
Simplify the result.
Tap for more steps…
Simplify each term.
Tap for more steps…
Raise 3 to the power of 2.
f(3)=2⋅9-5⋅3+4
Multiply 2 by 9.
f(3)=18-5⋅3+4
Multiply -5 by 3.
f(3)=18-15+4
f(3)=18-15+4
Simplify by adding and subtracting.
Tap for more steps…
Subtract 15 from 18.
f(3)=3+4
Add 3 and 4.
f(3)=7
f(3)=7
The final answer is 7.
7
7
The y value at x=3 is 7.
y=7
Graph the parabola using its properties and the selected points.
xy-1110454782237
xy-1110454782237
Graph the parabola using its properties and the selected points.
Direction: Opens Up
Vertex: (54,78)
Focus: (54,1)
Axis of Symmetry: x=54
Directrix: y=34
xy-1110454782237
Graph j(x)=2x^2-5x+4

Download our
App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Scroll to top