The graphs of the quadratic functions f(x) = 6 - 10x² and g(x) = 8 - (x-2)² are provided below. Observe there are TWO lines simultaneously tangent to both graphs. The one easier to imagine is tangent at points near the tops of the parabolas. Place a ruler on the screen to see where it is approximately. The other one should be on the left of the parabolas. It is steeper and has a larger slope. In this question, you will find their equations. You can start this question by setting the points of tangencies as (a,f(a)) and (b,g(b)), for example. Then, try to find equations (hint: slope) involving the unknowns a and b. 10 7.5 2 2 4 -2.5 -5 -7.5 -10 (a) The line simultaneously tangent to both graphs having the LARGEST slope has equation: (Two decimal places of accuracy.) × ×+ y = × . (b) The other line simultaneously tangent to both graphs has equation: (Two decimal places of accuracy.) y = x +
The graphs of the quadratic functions f(x) = 6 - 10x² and g(x) = 8 - (x-2)² are provided below. Observe there are TWO lines simultaneously tangent to both graphs. The one easier to imagine is tangent at points near the tops of the parabolas. Place a ruler on the screen to see where it is approximately. The other one should be on the left of the parabolas. It is steeper and has a larger slope. In this question, you will find their equations. You can start this question by setting the points of tangencies as (a,f(a)) and (b,g(b)), for example. Then, try to find equations (hint: slope) involving the unknowns a and b. 10 7.5 2 2 4 -2.5 -5 -7.5 -10 (a) The line simultaneously tangent to both graphs having the LARGEST slope has equation: (Two decimal places of accuracy.) × ×+ y = × . (b) The other line simultaneously tangent to both graphs has equation: (Two decimal places of accuracy.) y = x +
Chapter9: Quadratic Equations And Functions
Section9.6: Graph Quadratic Functions Using Properties
Problem 9.91TI: Find the intercepts of the parabola whose function is f(x)=3x2+4x+4.
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Transcribed Image Text:The graphs of the quadratic functions f(x) = 6 - 10x² and g(x) = 8 - (x-2)² are provided below. Observe there are TWO lines simultaneously tangent to both graphs. The one easier to imagine is tangent at points near the tops of the parabolas. Place a ruler on the screen to see
where it is approximately. The other one should be on the left of the parabolas. It is steeper and has a larger slope.
In this question, you will find their equations. You can start this question by setting the points of tangencies as (a,f(a)) and (b,g(b)), for example. Then, try to find equations (hint: slope) involving the unknowns a and b.
10
7.5
2
2
4
-2.5
-5
-7.5
-10
(a) The line simultaneously tangent to both graphs having the LARGEST slope has equation: (Two decimal places of accuracy.)
× ×+
y =
× .
(b) The other line simultaneously tangent to both graphs has equation: (Two decimal places of accuracy.)
y =
x +
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