### 1.6 Determine a Quadratic Equation Given its Roots

```1.6 Determine a Quadratic Equation Given its Roots – Worksheet MCR3U Jensen 1) Find the equation of a quadratic function that has the given x-­‐intercepts and contains the given point. Express each function in factored form. a) -­‐3 and 5, point (4, -­‐3) b) -­‐4 and 7, point (-­‐3, -­‐12) 2) Express each function from #1 in standard form. a) b) 3) Find the equation of a quadratic function that has the given x-­‐intercepts and contains the given point. Express each function in standard form. a) 1 ± 11 , point (4, -­‐6) b) −2 ± 7, point (1, 2) 4) Find the equation of the quadratic function that has zeros at 3 and -­‐1 and contains the point (1, -­‐2). Express the function in vertex form. 5) Determine the equation in standard form for each quadratic function shown. a) b) 6) An arch of a highway overpass is in the shape of a parabola. The arch spans a distance of 12 meters from one side of the road to the other. The height of the arch is 8 meters at a horizontal distance of 2 meters from each side of the arch. a) Sketch the quadratic function if the vertex of the parabola is on the y-­‐axis and the road is along the x-­‐
axis. b) Use this information to determine the function that models the arch. c) Find the maximum height of the arch to the nearest tenth of a meter. Answers !
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1) a) 𝑓 𝑥 = ! (𝑥 + 3)(𝑥 − 5) b) 𝑓 𝑥 = ! (𝑥 + 4)(𝑥 − 7) !
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2) a) 𝑓 𝑥 = ! 𝑥 ! − ! 𝑥 − ! b) 𝑓 𝑥 = ! 𝑥 ! − ! 𝑥 − ! 3) a) 𝑓 𝑥 = 3𝑥 ! − 6𝑥 − 30 b) 𝑓 𝑥 = 𝑥 ! + 4𝑥 − 3 !
4) 𝑓 𝑥 = ! 𝑥 − 1 ! − 2 !
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5) a) 𝑓 𝑥 = − ! 𝑥 ! + ! 𝑥 + 3 b) 𝑓 𝑥 = −4𝑥 ! − 8𝑥 + 60 !
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6) b) 𝑓 𝑥 = − ! 𝑥 ! + ! c) 14.4 m ```