Find the vertex, vertex form, and axis of symmetry for
x^2+2x=35
The quadratic you entered is not in standard form:
ax2 + bx + c = 0
Subtract 35 from both sides
x2+2x - 35 = 35 - 35x2+2x - 35 = 0
Set up the a, b, and c values:
a = 1, b = 2, c = -35
Vertex of a parabola
(h,k) where y = a(x - h)2 + k
Use the formula rule.
Our equation coefficients are a = 1, b = 2
The formula rule determines h
h = Axis of Symmetry
| h = | -b |
| 2a |
Plug in -b = -2 and a = 1
| h = | -(2) |
| 2(1) |
| h = | -2 |
| 2 |
h = -1 ← Axis of Symmetry
Calculate k
k = ƒ(h) where h = -1
ƒ(h) = (h)2(h)35=
ƒ(-1) = (-1)2(-1)35=
ƒ(-1) = 1 - 2 - 35
ƒ(-1) = -36
Our vertex (h,k) = (-1,-36)
Determine our vertex form:
The vertex form is: a(x - h)2 + k
Vertex form = (x + 1)2 - 36
Final Answer
Axis of Symmetry: h = -1
vertex (h,k) = (-1,-36)
Vertex form = (x + 1)2 - 36
vertex (h,k) = (-1,-36)
Vertex form = (x + 1)2 - 36
Test Your Knowledge?
- What is the formula for a quadratic equation?___When does the quadratic parabola open concave up?___How are the discriminant and quadratic solution related?
Common Core State Standards In This Lesson
HSN.CN.C.7, HSA.SSE.B.3.A, HSA.SSE.B.3.B, HSA.REI.B.4, HSA.REI.B.4.A, HSF.IF.C.8.A
What is the Answer?
Axis of Symmetry: h = -1
vertex (h,k) = (-1,-36)
Vertex form = (x + 1)2 - 36
vertex (h,k) = (-1,-36)
Vertex form = (x + 1)2 - 36
How does the Quadratic Equations and Inequalities Calculator work?
Free Quadratic Equations and Inequalities Calculator - Solves for quadratic equations in the form ax2 + bx + c = 0. Also generates practice problems as well as hints for each problem.
* Solve using the quadratic formula and the discriminant Δ
* Complete the Square for the Quadratic
* Factor the Quadratic
* Y-Intercept
* Vertex (h,k) of the parabola formed by the quadratic where h is the Axis of Symmetry as well as the vertex form of the equation a(h - h)2 + k
* Concavity of the parabola formed by the quadratic
* Using the Rational Root Theorem (Rational Zero Theorem), the calculator will determine potential roots which can then be tested against the synthetic calculator.
This calculator has 4 inputs.
* Solve using the quadratic formula and the discriminant Δ
* Complete the Square for the Quadratic
* Factor the Quadratic
* Y-Intercept
* Vertex (h,k) of the parabola formed by the quadratic where h is the Axis of Symmetry as well as the vertex form of the equation a(h - h)2 + k
* Concavity of the parabola formed by the quadratic
* Using the Rational Root Theorem (Rational Zero Theorem), the calculator will determine potential roots which can then be tested against the synthetic calculator.
This calculator has 4 inputs.
What 5 formulas are used for the Quadratic Equations and Inequalities Calculator?
y = ax2 + bx + c
(-b ± √b2 - 4ac)/2a
h (Axis of Symmetry) = -b/2a
The vertex of a parabola is (h,k) where y = a(x - h)2 + k
(-b ± √b2 - 4ac)/2a
h (Axis of Symmetry) = -b/2a
The vertex of a parabola is (h,k) where y = a(x - h)2 + k
What 9 concepts are covered in the Quadratic Equations and Inequalities Calculator?
- complete the square
- a technique for converting a quadratic polynomial of the form ax2 + bx + c to a(x - h)2 + k
- equation
- a statement declaring two mathematical expressions are equal
- factor
- a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n.
- intercept
- parabola
- a plane curve which is approximately U-shaped
- quadratic
- Polynomials with a maximum term degree as the second degree
- quadratic equations and inequalities
- rational root
- vertex
- Highest point or where 2 curves meet
