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6.4 Quadratic Formula Worksheet #1 MPM2D Jensen
1. Use the quadratic formula to solve each equation. Express answers as exact roots. a) 𝑦 = 7𝑥! + 24𝑥 + 9 = 0 b) 𝑦 = 2𝑥! + 4𝑥 − 7 = 0 c) 𝑦 = 4𝑥! − 12𝑥 + 9 = 0 d) 2𝑥! − 7𝑥 = −4 (remember to set = 0) e) 3𝑥! + 5𝑥 = 1 f) 16𝑥! + 24𝑥 = −9
2. Use the quadratic formula to solve. Express your answers as exact roots and as approximate roots, rounded to the nearest hundredth. a) 3𝑥! + 14𝑥 + 5 = 0 b) 8𝑥! + 12𝑥 + 1 = 0 c) 4𝑥! − 7𝑥 − 1 = 0 d) 10𝑥! − 45𝑥 − 7 = 0 e) −5𝑥! + 16𝑥 − 2 = 0 f) −6𝑥! + 17𝑥 + 5 = 0
4. For each quadratic relation, state the coordinates of the vertex and the direction of opening. Then, determine how many x-‐intercepts the relation has. a) 𝑦 = 𝑥 − 3 ! + 2 b) 𝑦 = − 𝑥 − 2 ! + 4 c) 𝑦 = 2 𝑥 + 4 ! − 5 d) 𝑦 = −2 𝑥 + 3 ! − 1 e) 𝑦 = 𝑥 − 5 !
Answers: 1. a) −3, !!
! b) !!± !"
! c) !
! d) !± !"
! e) !!± !"
! f) !!
!
2) a) !!± !"
!;−0.39,−4.28 b) !!± !
!;−0.09,−1.41 c) !± !"
!; 1.88,−0.13
d) !"± !"#$
!"; 4.65,−0.15 e) !!"± !"#
!!"; 0.13, 3.07 f) !"± !"#
!"; 3.1,−0.27
4. a) (3,2); opens up; no x-‐intercepts b) (2,4); opens down; two x-‐intercepts c) (-‐4,-‐5); opens up; two x-‐intercepts d) (-‐3,-‐1); opens downward; no x-‐intercepts e) (5,0); opens up; one x-‐intercept