5.5 Solving Problems with Quadratic Relations Standard form ...
5.5 Solving Problems with Quadratic Relations Standard form ...
5.5 Solving Problems with Quadratic Relations Standard form ...
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<strong>5.5</strong> <strong>Solving</strong> <strong>Problems</strong> <strong>with</strong> <strong>Quadratic</strong> <strong>Relations</strong><br />
<strong>Standard</strong> <strong>form</strong> Factored <strong>form</strong> Vertex <strong>form</strong><br />
y = ax 2 + bx + c y = a(x s)(x t) y = a(x h) 2 + k<br />
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1. Write each equation in vertex <strong>form</strong>.<br />
a) y = (x 3)(x + 1) b) y = 3(5 x)(3 x)<br />
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2. a) Write the quadratic relation y = x 2 4x 5 in vertex <strong>form</strong>.<br />
b) Describe the trans<strong>form</strong>ations you would apply to y = x 2 .<br />
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3. Write each equation in factored <strong>form</strong>.<br />
a) y = (x 1) 2 9 b) y = 2(x + 2) 2 32<br />
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Application<br />
4. The Next Cup coffee shop sells a special blend of coffee for $2.60 per<br />
mug. The shop sells about 200 mugs per day. Customer surveys show that<br />
for every $0.05 decrease in the price, the shop will sell 10 more mugs per day.<br />
a) Determine the maximum daily revenue from the coffee sales and the price<br />
per mug for this revenue.<br />
b) Write an equation in both standard <strong>form</strong> and vertex <strong>form</strong> to<br />
model this problem.<br />
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Communication<br />
5. Without calculating, determine the number of zeros for each graph. Explain<br />
your answers<br />
a) y = (x 3) 2 b) y = 2(x + 1) 2 + 4 c) y = (x 6) 2 + 1<br />
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Thinking<br />
Rebecca has a difficult golf shot to make. Her ball is 120 m from the hole. She wants<br />
the ball to land 10 m in front of the hole, so it can roll to the hole. A 15 m<br />
tree is between her ball and the hole 40 m from the hole and 80 m from her ball.<br />
With the base of the tree as the origin, write an algebraic expression to model the<br />
height of the ball if it just clears the top of the tree.<br />
Find the coordinates of the vertex of your model. Interpret the position the of vertex.<br />
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