Quadratic Graph Example: y=ax²+c
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- Graphing y=ax2+cy=ax^2+cy=ax2+c The graphs of y=ax2y=ax^2y=ax2 and y=ax2+cy=ax^2+cy=ax2+c are almost identical. The only difference between these functions is the ccc term. The …
By Ben Ferrara, Vatsal Ojha, Alex Federspiel, Jonathan Heller, Caroline K, Anusha Rahman
- Remember that the general form for a quadratic expression is: y=ax2+bx+cy=ax^2+bx+cy=ax2+bx+c where xxx is unknown (a variable), aaa and bbb are coefficients (numbers in front o…
By Hannah Bonville, Vatsal Ojha, Alex Federspiel, Jonathan Heller, Anusha Rahman
- (Video) Graphing Quadratic Functions - 1 by mathman1024 This by mathman1024 covers graphing quadratic functions. Summary\large{\text{Summary}}Summary A quadratic function is a f…
By Alex Federspiel, Vatsal Ojha, Amy Feraco, Jonathan Heller, Anusha Rahman
Problems 35
- At what point does the graph y=12x2−2y=\frac{1}{2}x^2 -2y=21x2−2 intersect the yyy-axis?
- What is the equation of the blue graph shown above?
- If the quadratic functions y1(x)=2x2+7y_1(x)=2x^2+7y1(x)=2x2+7 and y2(x)=2x2−2+cy_2(x)=2x^2-2+cy2(x)=2x2−2+c are identical, what does ccc equal?
- Concept Question: If a quadratic function has a graph of the form y=ax2+cy=ax^2 +cy=ax2+c, and aaa is negative, will the y-intercept of the graph be above or below the xxx-axis?
- What is the equation of the blue graph (A)?
- Graphed above are: y=0.5x2+1y=0.5x^2+1y=0.5x2+1 y=2x2+1y=2x^2+1y=2x2+1 y=x2−2y=x^2-2y=x2−2 y=0.5x2−2y=0.5x^2-2y=0.5x2−2 Which function f(x)f(x)f(x) is graphed in red?
- What is the y-intercept of y=3(−12x2+2)−5y=3\left(-\frac{1}{2}x^2+2\right)-5y=3(−21x2+2)−5?
- What is the equation of the red graph shown above?
- A spaceship is traveling around LV-426 to survey it. The navigational computer places the moon's center as the origin. The moon has a diameter of 216021602160 miles and the vert…
- Consider the quadratic equation y=ax2+cy=ax^2+cy=ax2+c. If a>0a>0a>0, what is the minimum yyy-value of the graph?
- Which two parabolas are symmetric to one another about the xxx-axis?
- For what value of aaa does the function f(x)=ax2+2f(x)=ax^2+2f(x)=ax2+2 pass through the point (1,4)(1,4)(1,4)?
- For what value of aaa does the function f(x)=ax2+2f(x)=ax^2+2f(x)=ax2+2 pass through the point (1,0)(1,0)(1,0)?
- Consider the above graph of f(x)=2x2+1f(x)=2x^2+1f(x)=2x2+1 (in red) and g(x)=2x2−1g(x)=2x^2-1g(x)=2x2−1 (in blue). Which of the following is true? (Check all that apply.)
- Consider the above graph of f(x)=−2x2+2f(x)=-2x^2+2f(x)=−2x2+2 (in red) and g(x)=−2x2g(x)=-2x^2g(x)=−2x2 (in blue). Which of the following is true? (Check all that apply.)
- Which coordinate is the vertex of any quadratic function of the form y=ax2+cy=ax^2+cy=ax2+c?
- If f(x)=ax2+cf(x)=ax^2+cf(x)=ax2+c is a quadratic function, what must be true of aaa?
- Which two parabolas are symmetric to one another about the xxx-axis?
- For what value of ccc does the function f(x)=2x2+cf(x)=2x^2+cf(x)=2x2+c pass through the point (2,4)(2,4)(2,4)?
- Consider the above graph of f(x)=x2+1f(x)=x^2+1f(x)=x2+1 and g(x)=−x2−1g(x)=-x^2-1g(x)=−x2−1. Which of the following is true? (Check all that apply.)
- Consider the quadratic equation y=ax2+cy=ax^2+cy=ax2+c. If a<0a<0a<0, what is the maximum yyy-value of the graph?
- If fff is a quadratic function of the form ax2+cax^2+cax2+c, what is the maximum number of real-numbered roots the function can have?
- If fff is a quadratic function of the form ax2+cax^2+cax2+c, what is the minimum number of real-numbered roots the function can have?
- If fff is a quadratic function of the form ax2+cax^2+cax2+c and has exactly 111 real-numbered root, which one of the following must be true?
- If fff is a quadratic function of the form ax2+cax^2+cax2+c and has exactly 222 real-numbered roots, which one of the following must be true?
- If fff is a quadratic function of the form ax2+cax^2+cax2+c and no real-numbered roots, which one of the following must be true?
- Compared to y=2x2y=2x^2y=2x2, how many units would y=2x2+5y=2x^2+5y=2x2+5 be shifted?
- Compared to y=5x2y=5x^2y=5x2, how many units would y=5x2−2y=5x^2-2y=5x2−2 be shifted?
- 5y=25x2+255y = 25x^2 +255y=25x2+25 is a parabola that has been shifted upward 555 units from 5y=25x25y=25x^25y=25x2. Which term determined the number of units shifted?
- y=ax2+cy=ax^2 + cy=ax2+c and c<0c<0c<0. Which direction is the parabola shifted, compared to y=ax2y=ax^2y=ax2?
- Which direction is the parabola shifted?
- Parabola A:y=3x2Parabola B:y=3x2+9\begin{array}{lrcl} \text{Parabola A:}&y&=&3x^2 \\ \text{Parabola B:}&y&=&3x^2 + 9 \end{array}Parabola A:Parabola B:yy==3x23x2+9 How many u…
- Parabola A:y=4x2+12Parabola B:y=4x2+16\begin{array}{lrcl} \text{Parabola A:}&y&=&4x^2 +12 \\ \text{Parabola B:}&y&=&4x^2 + 16 \end{array}Parabola A:Parabola B:yy==4x2+124x2+1…
- Parabola A:y=2x2−8Parabola B:y=2x2+6\begin{array}{lrcl} \text{Parabola A:}&y&=&2x^2 - 8 \\ \text{Parabola B:}&y&=&2x^2 + 6 \end{array}Parabola A:Parabola B:yy==2x2−82x2+6 Ho…
- Parabola A:y=14x2+7Parabola B:y=14x2−35\begin{array}{lrcl} \text{Parabola A:}&y&=&14x^2 + 7 \\ \text{Parabola B:}&y&=&14x^2 - 35 \end{array}Parabola A:Parabola B:yy==14x2+714…