How many outcomes have exactly 1 head?
2 answers:
You might be interested in
Answer:
The values of a and b are 1 and -8
Step-by-step explanation:
Let us solve the question by comparing the two sides.
∵ x² + 2x - 7 = (x + a)² + b
→ Let us solve the bracket on the right side
∵ (x + a)² = (x)(x) + 2(x)(a) + (a)(a)
∴ (x + a)² = x² + 2ax + a²
→ Substitute it in the right side above
∴ x² + 2x - 7 = x² + 2ax + a² + b
→ Compare the like terms on both sides (terms of x², terms of x
and numerical terms)
∵ The terms of x are 2x and 2ax
→ Equate them
∵ 2x = 2ax
→ Divide both sides by 2x
∴ =
∴ 1 = a
∴ The value of a = 1
∵ The numerical terms are -7 and a² + b
→ Equate them
∵ -7 = a² + b
→ Substitute a by 1
∴ -7 = (1)² + b
∴ -7 = 1 + b
→ Subtract 1 from both sides
∵ -7 - 1 = 1 - 1 + b
∴ -8 = b
∴ The value of b = -8
∴ The values of a and b are 1 and -8
Answer:
A. (-1, -4)
Step-by-step explanation:
The vertex can be found by converting the equation from standard form to vertex form.
<h3>Vertex</h3>Considering the x-terms, we have ...
y = (x^2 +2x) -3
where the coefficient of x is 2. Adding (and subtracting) the square of half that, we get ...
y = (x^2 +2x +(2/2)^2) -3 -(2/2)^2
y = (x +1)^2 -4
Compare this to the vertex form equation ...
y = a(x -h)^2 +k
which has vertex (h, k).
We see that h=-1 and k=-4. The vertex is (h, k) = (-1, -4).
On the attached graph, the vertex is the turning point, the minimum.
Answer:
Step-by-step explanation:
The equation of a quadratic function is given as:
ax² + bx + c = 0
where a, b and c are the coefficient in the quadratic equation.
The axis of symmetry of the quadratic equation is given as:
To get the equation for a, we have to make a the subject of formula: