Quadratics BARNES

Question 1

Quadratic formula

Answer 1

-b±√(b²-4ac) / (2a)

Question 2

What is the discriminant

Answer 2

b² - 4ac

Question 3

if b² - 4ac > 0

Answer 3

there are 2 distinct solutions

Question 4

if b2 - 4ac = 0

Answer 4

there is one repeated solution

Question 5

if b2 - 4ac < 0

Answer 5

there are no real solutions

Question 6

solve
x4 - 3x2 - 4 = 0

Answer 6

let y = x^2
x = +2 or -2

Question 7

what are disguised quadratics

Answer 7

equations that become quadratic by making a substitution

Question 8

solve
x - 10√x + 24 = 0

Answer 8

let y = √x
x = 16 or 36

Question 9

An expression x2 + bx + c can be rewritten by completing the square

Answer 9

(x + p)^2 + q
where p = b/2, q = c - p^2

Question 10

We use the form
a(x + p)^2 + q
to identify the vertex (turning point) of a quadratic

Answer 10

Vertex at (-p, q)

Question 11

minimum if
( a(x + p)^2 + q )

Answer 11

a > 0 (happy face graph)

Question 12

maximum if
( a(x + p)^2 + q )

Answer 12

a < 0 (sad face graph)

Question 13

Quadratic graphs have a vertical line of symmetry at

Answer 13

x = -p

Question 14

how to find y-intercept

Answer 14

y-value when x = 0

Question 15

how to find roots

Answer 15

solutions for x, when y = 0
- can be 2, 1 or 0 real roots
- found by factorising or formula

Question 16

5 + 3x - 2x^2 < 1 - 4x
find inequality

Answer 16

x < -0.5
or
x > 4

Question 17

Find the set of values for k for which the equation 2x^2 - (k + 1)x + 5 - k = 0
has two distinct real solutions

Answer 17

k < -13
or
k > 3

Question 18

intersections between curves are found by

Answer 18

solving simultaneous equations

Question 19

Find the coordinates of the points of intersection
between the graphs

x+2y = 3
y^2 + 2xy + 9 = 0

Answer 19

(-3,3) and (5,-1)